名校
解题方法
1 . 已知椭圆
的左,右焦点分别为
,下顶点为A,点M在直线
上.
(1)若
,线段AM 的中点在x轴上,求M 的坐标;
(2)若直线l与y轴交于B,直线AM 经过右焦点
,在
中有一个内角的余弦值为
,求b的值;
(3)若
,直线 l与椭圆Γ没有公共点,在椭圆Γ上存在一点
,
,点P到l的距离为d,且
,当a变化时,求d的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e31f17d3eae2f76500ee2e8f955865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a029686de8da4b04df32af401089a9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa5584ebddd742ffcf0e58a4c3b108c.png)
(2)若直线l与y轴交于B,直线AM 经过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc97864dd9abe8013867fdd6b9562c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386ddd7cba3dc92cb43743f663ae63d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0ca9a39621967d7ba5629ea9b12d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c318dc642320a42ad8f7c565246858b5.png)
您最近一年使用:0次
2 . 已知椭圆
的长轴长为
,且过点
.记椭圆的左右焦点分别为
,
,过点
的直线l交椭圆C于不同的两点P、Q.
(1)求椭圆的标准方程;
(2)若以线段PQ为直径的圆过点
,求直线l的方程;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.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/40630a669f4eedf626bc24851df10c85.png)
(1)求椭圆的标准方程;
(2)若以线段PQ为直径的圆过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddd0a7d62c553d3ad17e2be6e8fdaf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
3 . 已知曲线
,
为
上一点,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6723029f949f6c91b78f0870008b463f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.曲线![]() |
B.![]() ![]() |
C.存在点![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2024-02-11更新
|
157次组卷
|
2卷引用:福建省宁德市2023-2024学年高二上学期期末质量检测数学试题
解题方法
4 . 设椭圆
的右顶点为
,上顶点为
.已知椭圆的离心率为
,
.
(1)求椭圆的方程;
(2)设直线
与椭圆交于
,
两点,
与直线
交于点
,且点
,
均在第四象限.若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](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/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b685dfb277b4d68a4c390152339898e.png)
(1)求椭圆的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b408a02331b54b3286d0eefb29908ee2.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/0f85fca60a11e1af2bf50138d0e3fe62.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35128bd3771c59cd37c49f6d2b8799d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5 . 已知椭圆
的右顶点
,过点
的直线
与椭圆
交于
,
两点(
,
异于点
),当直线
与
轴垂直时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/5772faf0-2aa5-4366-8bd5-84be3bc19289.png?resizew=135)
(1)求椭圆C的方程;
(2)求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd67f4ff7cb2455222ec40bc1d8bf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0bc3a43265b63b6964476ca327fab.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/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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158db3f561cb7fc2cc6b4a884be80c93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/5772faf0-2aa5-4366-8bd5-84be3bc19289.png?resizew=135)
(1)求椭圆C的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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2024-01-23更新
|
606次组卷
|
4卷引用:四川省凉山州安宁河联盟2023-2024学年高二上学期期末联考数学试题
名校
6 . 已知中心在原点,离心率为
的椭圆的一个焦点为圆
:
的圆心,点
是椭圆上第三象限内的一点,过点
作两条斜率之积为
的直线都与圆相切时,点
的坐标是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a8a4e3f7b82e70a09d8c6550ad1a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
7 . 已知离心率
的椭圆
的中心在原点
,焦点在
轴上,直线
交
于
、
两点,且
,其中点
.
(1)求
的面积
的最大值,并求此时椭圆
的方程;
(2)对于(1)的椭圆
上,若存在不同的两点关于直线
对称,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234e7679481ec0d01c915b7fbb71891d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](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/ea60b7fd21ff012243a74f196d379501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2f117dc9adcb8fa7acf25bd2cbf283.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)对于(1)的椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce37928403e28dea457850542edd414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
8 . 已知椭圆
:
和圆
:
,点
是圆
上的动点,过点
作椭圆的切线
,切点为A,B.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/0947386b-027e-4bff-9f08-2a5a4919bd44.png?resizew=164)
(1)若点
的坐标为
,证明:直线
;
(2)求O到直线
的距离的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/44434b647ec546fe787e2164e0be6cd2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/0947386b-027e-4bff-9f08-2a5a4919bd44.png?resizew=164)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fed700b7a3ab2ee7fbae12507033af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
(2)求O到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-01-05更新
|
115次组卷
|
2卷引用:四川省遂宁市射洪中学校2023-2024学年高二上学期12月月考数学试题
解题方法
9 . 已知椭圆
与椭圆
有相同的离心率,且
为
的上顶点.
(1)求
的标准方程;
(2)设斜率存在且经过原点的直线l交
于
两点,直线
与
异于点A的另一交点分别为点M,N,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540bff14a4d81fb9e32114522c57ba9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设斜率存在且经过原点的直线l交
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67660ecd88652c3d96dce1ee5da31524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e712b3a3a835b6d32e51fde2cae0b178.png)
您最近一年使用:0次
2024-01-03更新
|
134次组卷
|
2卷引用:河南省青桐鸣2023-2024学年高二上学期12月联考数学试题
解题方法
10 . 已知中心在坐标原点,焦点在x轴上的椭圆M的离心率为
,椭圆上异于长轴顶点的任意点A与左右两焦点
,
构成的三角形中面积的最大值为
.
(1)求椭圆M的标准方程;
(2)若A与C是椭圆M上关于x轴对称的两点,连接
与椭圆的另一交点为B,求证:直线AB与x轴交于定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆M的标准方程;
(2)若A与C是椭圆M上关于x轴对称的两点,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c738d79a58541893b80507871c348f66.png)
您最近一年使用:0次