名校
解题方法
1 . 已知结论:椭圆
上一点
处切线方程为
.试用此结论解答下列问题.如图,已知椭圆
:
的右焦点为
,原点为
,椭圆的动弦AB过焦点
且不垂直于坐标轴,弦
的中点为
,椭圆
在点A,B处的两切线的交点为
.
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a271c22e34d4df61636ab3052a8e0ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1185a977aa9dc61d23db4b658126f8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/b9703fbb-7e2a-404b-bdfe-c1c16369ef43.png?resizew=161)
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfba099195b252ab0faba0d8360fae98.png)
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名校
解题方法
2 . 已知
,
.
(1)证明:
总与
和
相切;
(2)在(1)的条件下,若
与
在y轴右侧相切于A点,与
在y轴右侧相切于B点.直线
与
和
分别交于P,Q,M,N四点.是否存在定直线
使得对任意题干所给a,b,总有
为定值?若存在,求出
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417c20f9751c8e956eb19c23f35bb5a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ac6f5e3bea8daa9e23abad1e81113.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcaff1c3d13407048107680ba75d317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcaff1c3d13407048107680ba75d317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46d758ed2c2aa64e3bf3606d844ff8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
3 . 设
、
分别为椭圆
的左、右顶点,设
是椭圆下顶点,直线
与
斜率之积为
.
(1)求椭圆
的标准方程;
(2)若一动圆的圆心
在椭圆上运动,半径为
.过原点
作动圆
的两条切线,分别交椭圆于
、
两点,试证明
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242dc4cf2720b503e26ec8017d31444f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若一动圆的圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a9535f46dcbf08b03cd8b0539663e8.png)
您最近一年使用:0次
2022-05-21更新
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6卷引用:四川省遂宁市射洪中学校2023届高三下学期开学考试理科数学试题
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