名校
解题方法
1 . 已知线段
的端点
的坐标是
,端点
的运动轨迹是曲线
,线段
的中点
的轨迹方程是
.
(1)求曲线
的方程;
(2)已知斜率为
的直线
与曲线
相交于异于原点
的两点
直线
的斜率分别为
,
,且
证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6312d9085e90b6cebac7b5d95b83707b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/523a4b0a4a26ba0775429cfdc7ac1687.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b997a227ea03deef7008f2314252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac2cb390167b985c7c7d57294055964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9312074eb75e3ce0625c416bb8a81546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
2 . 在平面直角坐标系
中,已知两点
,动点
满足
,设点
的轨迹为
.如图,动直线
与曲线
交于不同的两点
(
均在
轴上方),且
.
(1)求曲线
的方程;
(2)当
为曲线
与
轴正半轴的交点时,求直线
的方程;
(3)是否存在一个定点,使得直线
始终经过此定点?若存在,求出定点的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c273f9be4092e52c919e87829bb30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b98083e9487cf0def4934715c2b2339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0e43b76bf316165e1ab3d210950ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/741488d8-5231-4ce3-9cc7-30b5ddd1a1af.png?resizew=170)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)是否存在一个定点,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:上海市曹杨第二中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
3 . 已知圆C与直线
相切于点
,且圆心C在x轴的正半轴上.
(1)求圆C的方程;
(2)过点
作直线交圆C于M,N两点,且M,N两点均不在x轴上,点
,直线BN和直线OM交于点G.证明:点G在一条定直线上,并求此直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e0fc0eb117d9504dcee30c86650c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedad6bb70631b944c69f8f0b02b35d6.png)
(1)求圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ba5cbb31299d683ac6c7dd795db85.png)
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解题方法
4 . 已知直线l:
和圆O:
相交于A,B两点.
(1)当
且
时,过点A,B分别作圆O的两条切线,求两切线的交点坐标;
(2)对于任意的实数k,在y轴上是否存在一点N,满足
?若存在,请求出此点坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6193fa0e3f05a9c411ed8dcd0a3fd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc64eaf4cd6737b000b28f1fcdd16c4b.png)
(2)对于任意的实数k,在y轴上是否存在一点N,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a42f8fdd353e8c83b34ee81c544fc.png)
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解题方法
5 . 已知圆心在
轴上的圆
与直线
切于点
,圆
.
(1)求圆
的标准方程.
(2)若圆
上两动点
,与坐标原点
所成角
,求线段
中点
的轨迹方程;
(3)已知
,圆
与
轴相交于两点
两点(点
在点
的右侧).过点
任作一条倾斜角不为0的直线与圆
相交于
两点.问:是否存在实数
,使得
?若存在,求出实数
值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bba5922f974abd7883d7a5dcddb8e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c3cde70f2d5b8b80b3acebbd71a79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f05e66538c245c0a24d90ef77f30fd.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1167767fd847678ef279f3e637f2828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5ce23462dfd28929430b74b9590940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
426次组卷
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2卷引用:湖南省长沙市实验中学2023-2024学年高二上学期第一次阶段性测试数学试题
6 . 已知定点
,
,动点M满足
.
(1)求动点M的轨迹C的方程;
(2)设
,过点T作与x轴不重合的直线l交曲线C于E、F两点.
(i)过点T作与直线l垂直的直线m交曲线C于G、H两点,求四边形EGFH面积的最大值;
(ii)设曲线C与x轴交于P、Q两点,直线PE与直线QF相交于点N,试讨论点N是否在定直线上,若是,求出该直线方程;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daec826bcf98e738a52fa34eb8a5e85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1400bea62e9e0bf6c924b796045b3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe585d05e3156dfeadf46144bd45b38.png)
(1)求动点M的轨迹C的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1400bea62e9e0bf6c924b796045b3948.png)
(i)过点T作与直线l垂直的直线m交曲线C于G、H两点,求四边形EGFH面积的最大值;
(ii)设曲线C与x轴交于P、Q两点,直线PE与直线QF相交于点N,试讨论点N是否在定直线上,若是,求出该直线方程;若不是,说明理由.
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7 . 已知圆
上两点
满足
,点
满足
,则下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccffb5750cd8d591f56a2708ffe9e560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a971599951255f3109e09753398e1529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417f81e550a7f99f6edd9cfaa6753163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60097cec26b613837579cff70a863a42.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.线段![]() ![]() |
D.过![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-10-10更新
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422次组卷
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2卷引用:黑龙江省哈尔滨师范大学附属中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
8 . 已知圆
的方程为
,直线
与圆
交于
两点.
(1)若坐标原点
到直线的距离为
,且
过点
,求直线
的方程;
(2)已知点
,
为
的中点,若
在
轴上方,且满足
,在圆
上是否存在定点
,使得
的面积为定值?若存在,求出
的面积;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbbc9c5353894f2c93c205c3ac04f03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/27/c20f2579-2601-44d8-9f2b-f1df4d774ea7.png?resizew=164)
(1)若坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3492b97c5b85da3965f86239ede4e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a297f399ee48fe07cd6aacc935a1c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cce6cac0fdd4b1a434af8bcaec8fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbbc9c5353894f2c93c205c3ac04f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4091ab879b17b7e65ca97fb0189364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5261a9730779339dc71818b9b6eff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5261a9730779339dc71818b9b6eff7.png)
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解题方法
9 . 设抛物线
与两坐标轴的交点分别记为M,N,G,曲线C是经过这三点的圆.
(1)求圆C的方程.
(2)过
作直线l与圆C相交于A,B两点,
(i)用坐标法证明:
是定值.
(ii)设
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e6893063df9d4188f3b7002664097d.png)
(1)求圆C的方程.
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
(i)用坐标法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be14af6ba191f83c422bd408900882b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397b6e8a1a21509f164d7b4b3382821.png)
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2023-10-08更新
|
569次组卷
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3卷引用:浙江省杭州市四校2023-2024学年高二上学期10月联考数学试题
名校
10 . 已知圆,直线
为直线
上一点,过点
作圆
的两条切线
,其中
为切点,且
最小.
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
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2023-10-05更新
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9卷引用:贵州省2023-2024学年高二上学期阶段性联考(一)数学试题
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