1 . 已知椭圆
:
,
,
为左右焦点,直线l过左焦点
与椭圆交于A,B两点,其中A在第一象限,记
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/2407d664-f5bd-480f-b43b-0084f5d2156c.png?resizew=173)
(1)若椭圆
的离心率为
,三角形
的周长为6,求椭圆
的方程;
(2)求证:
;
(3)直线
与椭圆交于另一点
,若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57654bf131df03b31d3d11b5b656c73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe197f95a36f68ee80f69ff5f4a26970.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/2407d664-f5bd-480f-b43b-0084f5d2156c.png?resizew=173)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227fb6f5f485e12ddad01ef7cb1e06d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a665b04ba8406d1f55bebb0cb7389c.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72404eb522c6cc692757b0855c2df865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708d0e76f524d0e8a48db01392faac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71eda28755639d00f9d24b95679d9496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de82aff5049dce8a3d56291dc2ae4af.png)
您最近一年使用:0次
名校
解题方法
2 . 圆
称为椭圆
的蒙日圆.已知椭圆
:
的离心率为
,
的蒙日圆方程为
.
(1)求
的方程;
(2)若
为
的左焦点,过
上的一点
作
的切线
,
与
的蒙日圆交于
,
两点,过
作直线
与
交于
,
两点,且
,证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49137970108f50350a3211aa0281faaf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb43ee1cddcc3e1773260a7ac1dc3fea.png)
您最近一年使用:0次
2023-12-16更新
|
271次组卷
|
5卷引用:河北省保定市部分高中2024届高三上学期12月期中联考数学试题
名校
解题方法
3 . 已知椭圆
的中心为
,离心率为
.圆
在
的内部,半径为
.
,
分别为
和圆
上的动点,且
,
两点的最小距离为
.
(1)建立适当的坐标系,求
的方程;
(2)
,
是
上不同的两点,且直线
与以
为直径的圆的一个交点在圆
上.求证:以
为直径的圆过定点.
![](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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80f580d0f5279d4a8fc07efdd9ca2e.png)
(1)建立适当的坐标系,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-04-03更新
|
1524次组卷
|
4卷引用:福建省晋江市季延中学2022-2023学年高二上学期期中考试数学试题
福建省晋江市季延中学2022-2023学年高二上学期期中考试数学试题福建省2022届高三诊断性检测数学试题(已下线)临考押题卷06-2022年高考数学临考押题卷(新高考卷)(已下线)必刷卷01-2022年高考数学考前信息必刷卷(新高考地区专用)