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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">如图，在平面直角坐标系中，抛物线<i>y</i>＝<i>ax</i></span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">+<i>bx</i>+<i>c</i>（<i>a</i>≠0）与<i>x</i>轴相交于<i>A</i>，<i>B</i>两点，与<i>y</i>轴相交于点<i>C</i>，直线<i>y</i>＝<i>kx</i>+<i>n</i>（<i>k</i>≠0）经过<i>B</i>，<i>C</i>两点，已知<i>A</i>（1，0），<i>C</i>（0，3），且<i>BC</i>＝5．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">（1）分别求直线<i>BC</i>和抛物线的解析式（关系式）；</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">（2）在抛物线的对称轴上是否存在点<i>P</i>，使得以<i>B</i>，<i>C</i>，<i>P</i>三点为顶点的三角形是直角三角形？若存在，请求出点<i>P</i>的坐标；若不存在，请说明理由．</span></span></span></span></span><br /> <img height="217" src="/uploads/meth/20210329/cf3e783c89eb44e056ac14da62b1cad4.png" width="197" />
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自主录题
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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">解：（1）∵<i>C</i>（0，3），即<i>OC</i>＝3，<i>BC</i>＝5，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴在Rt△<i>BOC</i>中，根据勾股定理得：<i>OB</i>＝</span></span></span></span></span><img height="24" src="/uploads/meth/20210329/b626c3e2cb0a9be5289922d444cd3d14.png" width="75" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">＝4，即<i>B</i>（4，0），</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">把<i>B</i>与<i>C</i>坐标代入<i>y</i>＝<i>kx</i>+<i>n</i>中，得：</span></span></span></span></span><img height="38" src="/uploads/meth/20210329/5965df0920813d68e4f26850f52cf277.png" width="60" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">解得：<i>k</i>＝﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/1ccfe4feae684d5db4c1951b4af32158.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，<i>n</i>＝3，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴直线<i>BC</i>解析式为<i>y</i>＝﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/bc3589a36968bfd66396826682649f25.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><span style="line-height:150%"><span style="font-family:宋体">+3；</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">由<i>A</i>（1，0），<i>B</i>（4，0），设抛物线解析式为<i>y</i>＝<i>a</i>（<i>x</i>﹣1）（<i>x</i>﹣4）＝<i>ax</i></span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">﹣5<i>ax</i>+4<i>a</i>，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">把<i>C</i>（0，3）代入得：<i>a</i>＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/7a34d7d3013195e3c73f84cc29003ff6.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">则抛物线解析式为<i>y</i>＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/d3707c0ecbf9fac16a60d7c63e6cc67c.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/40ea525e24048aadb225d33560a82116.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><span style="line-height:150%"><span style="font-family:宋体">+3；</span></span></span></span></span><br /> <br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">（2）存在．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">如图所示，分两种情况考虑：</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∵抛物线解析式为<i>y</i>＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/bd5a5a76cae4982330de288364da500e.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/0a79fb33a91b1b176d417f382e007139.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><span style="line-height:150%"><span style="font-family:宋体">+3，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴其对称轴<i>x</i>＝﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/e89fb1331f76e02e94cf9c8a253c3251.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">＝﹣</span></span></span></span></span><img height="73" src="/uploads/meth/20210329/4a661627c273bfb46469ae6fdef3e107.png" width="42" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/5fba7808d61a7e4a44bb93d23c1d79ff.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">当<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">1</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">C</span></span></i><span style="line-height:150%"><span style="font-family:宋体">⊥<i>CB</i>时，△<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">1</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">BC</span></span></i><span style="line-height:150%"><span style="font-family:宋体">为直角三角形，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∵直线<i>BC</i>的斜率为﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/d8848babd0e354bb726fcc0516d5142d.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴直线<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">1</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">C</span></span></i><span style="line-height:150%"><span style="font-family:宋体">斜率为</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/1a263a404edc600ca71db076167fa6ed.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴直线<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">1</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">C</span></span></i><span style="line-height:150%"><span style="font-family:宋体">解析式为<i>y</i>﹣3＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/a976630b23e6e41207b2644d62c6a265.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><span style="line-height:150%"><span style="font-family:宋体">，即<i>y</i>＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/4b83f0ca3b13797f6028b865fc5f9e50.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><span style="line-height:150%"><span style="font-family:宋体">+3，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">与抛物线对称轴方程联立得</span></span></span></span></span><img height="76" src="/uploads/meth/20210329/08e5ebb800d51f14289c1674a92861b9.png" width="67" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">解得：</span></span></span></span></span><img height="76" src="/uploads/meth/20210329/8efd58b14dd87509d553697a84d4ffe5.png" width="49" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">此时<i>P</i>（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/212fb293390800802d4748871be9b84f.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/dc6583d15bf6afceb3d2cf09e617bc85.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">）；</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">当<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">B</span></span></i><span style="line-height:150%"><span style="font-family:宋体">⊥<i>BC</i>时，△<i>BCP</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">为直角三角形，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">同理得到直线<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">B</span></span></i><span style="line-height:150%"><span style="font-family:宋体">的斜率为</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/ca93bc587a9d3775a57f8be17dd48eed.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴直线<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><i><span style="line-height:150%"><span style="font-family:宋体">B</span></span></i><span style="line-height:150%"><span style="font-family:宋体">方程为<i>y</i>＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/6a875ca6c1a3de7c5c86419911690a2f.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">（<i>x</i>﹣4）＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/dea1e1e5c888e4c241ff93caab08d040.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span style="line-height:150%"><span style="font-family:宋体">x</span></span></i><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/b2f0a19b7f68046bda070d0353f76060.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">与抛物线对称轴方程联立得：</span></span></span></span></span><img height="76" src="/uploads/meth/20210329/59e73f26623018215983e396aeecd728.png" width="80" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">解得：</span></span></span></span></span><img height="58" src="/uploads/meth/20210329/b2d454e447e27f858311291e78db1051.png" width="44" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">此时<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/6daff68a600b57287004143a7e48c88b.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，﹣2）．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">综上所示，<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">1</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/e77b72553d353b95d49881d863642bf8.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/18e08203caedf0813d73d973548d9df4.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">）或<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/a10ca3b32e32a1ec942c440eb0714130.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，﹣2）．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">当点<i>P</i>为直角顶点时，设<i>P</i>（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/0a1ea9e33c6bacb62416109ec54f5a24.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，<i>y</i>），</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∵<i>B</i>（4，0），<i>C</i>（0，3），</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>BC</i>＝5，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>BC</i></span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">＝<i>PC</i></span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">+<i>PB</i></span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">，即25＝（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/407086700c5cde2d4f419b547da15f09.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">）</span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">+（<i>y</i>﹣3）</span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">+（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/d6456a68e1f695de98a7aaea3b78c5c4.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">﹣4）</span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">+<i>y</i></span></span><sup><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sup><span style="line-height:150%"><span style="font-family:宋体">，解得<i>y</i>＝</span></span></span></span></span><img height="37" src="/uploads/meth/20210329/3356e5199f64d27715931604aeb4011f.png" width="57" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">∴<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">3</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/af2f81e270a2f04aec1970afdb2179b6.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="37" src="/uploads/meth/20210329/21b4ef687d9cd22af7e0673e97178d53.png" width="49" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">），<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">4</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/354d369c05ad498ae10c66c0ba0a200a.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="37" src="/uploads/meth/20210329/25776fd80aef3e7419b929bb6c369263.png" width="49" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">）．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">综上所述，<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">1</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/6b75401d26782d1f47538913a6bad5a5.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/39721b4fce708fbde6535cae46fea896.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">），<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">2</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/f4f4586b98934b445e2240ab8f0f9e04.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，﹣2），<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">3</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/67dc5a8bcdbc729feb95448c47e4f116.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="37" src="/uploads/meth/20210329/c44f015afc468cdef56a613db9f86aa6.png" width="49" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">），<i>P</i></span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">4</span></span></span></sub><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span></span></span><img height="35" src="/uploads/meth/20210329/eaa2072a1e850fcc8336d268954def31.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span><img height="37" src="/uploads/meth/20210329/d88835a1b16f7f055da616110d6efd82.png" width="49" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:宋体">）．</span></span></span></span></span><br /> <img height="227" src="/uploads/meth/20210329/fac0412c17c49b451204c2e12ba49dfd.png" width="197" /><br />
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本题考查了"二次函数综合应用 勾股定理 二次函数的动点问题 求二次函数的解析式 "，属于"综合题"，熟悉知识点是解题的关键
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