解题方法
1 . 已知椭圆
的右焦点为F,椭圆
.
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967973908578304/2969179699650560/STEM/edae2333f4f24b1ea933ca0d5f97c53b.png?resizew=182)
(1)求
的离心率;
(2)如图:直线
交椭圆
于A,D两点,交椭圆E于B,C两点.
①求证:
;
②若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff1455a4045eb93f482c0751840aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3a3269dd7a4539c7eec25df816b60a.png)
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967973908578304/2969179699650560/STEM/edae2333f4f24b1ea933ca0d5f97c53b.png?resizew=182)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)如图:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44c7d3a8499af18da17231d6b898274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495021c7da1c77e6ed1d1dd30e0be7bc.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a5569b9f84d91f16f1762ef1e6d0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
您最近一年使用:0次
解题方法
2 . 已知椭圆
的下顶点
和右顶点
都在直线
上.
(1)求椭圆方程及其离心率;
(2)不经过点
的直线
交椭圆
于两点
,过点
作
轴的垂线交
于点
,点
关于点
的对称点为
.若
三点共线,求证:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e6f7933ab5f681124d3be486b39964.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/8de0634718ca1ccbeccc53927429cf49.png)
(1)求椭圆方程及其离心率;
(2)不经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621c56b8094065a66f61bdbda345b56.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c838ef44cf5bdd730436b074b3f3909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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2022-03-29更新
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3卷引用:北京市海淀区2022届高三一模数学试题
名校
解题方法
3 . 已知椭圆的两焦点分别为
、
,椭圆上的动点
满足
,
、
分别为椭圆的左、右顶点,
为坐标原点.
(1)求椭圆的方程及离心率;
(2)若直线
与
交于点
,
与
轴交于点
,
与
的交点为
,求证:
、
、
、
四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58be748090ab0d02056ae539212038b.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/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆的方程及离心率;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82457835249314f216eabc9b7261ae81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
2021-05-29更新
|
1351次组卷
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5卷引用:北京市中央民族大学附属中学2021届高三三模数学试题
北京市中央民族大学附属中学2021届高三三模数学试题(已下线)第46讲 解析几何中的四点共圆问题-2022年新高考数学二轮专题突破精练(已下线)专题38 圆锥曲线中的圆问题-2(已下线)专题04 圆锥曲线经典题型全归纳(3)北京卷专题23平面解析几何(解答题部分)
4 . 已知直线l经过椭圆C:
的左焦点
和下顶点,坐标原点O到直线l的距离为
.
(Ⅰ)求椭圆C的离心率;
(Ⅱ)若椭圆C经过点
,A,B是椭圆C上的两个动点,且
的角平分线总是垂直于y轴,求证:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c92ae7a5cd7a0e337b758f0e443cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46947da34351a77f846092424cf7bb39.png)
(Ⅰ)求椭圆C的离心率;
(Ⅱ)若椭圆C经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
解题方法
5 . 已知椭圆M:
(a>b>0)过A(-2,0),B(0,1)两点.
(1)求椭圆M的离心率;
(2)设椭圆M的右顶点为C,点P在椭圆M上(P不与椭圆M的顶点重合),直线AB与直线CP交于点Q,直线BP交x轴于点S,求证:直线SQ过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
(1)求椭圆M的离心率;
(2)设椭圆M的右顶点为C,点P在椭圆M上(P不与椭圆M的顶点重合),直线AB与直线CP交于点Q,直线BP交x轴于点S,求证:直线SQ过定点.
您最近一年使用:0次
2021-05-02更新
|
3904次组卷
|
14卷引用:北京市海淀区2021届高三下学期期中数学试题
北京市海淀区2021届高三下学期期中数学试题山东省潍坊市2021届高三二模考试数学模拟试题北京市海淀区2021届高三一模数学试题(新高考)2021届高考考前数学冲刺卷试题(一)(已下线)专题3.7 椭圆的综合问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线)第3讲 圆锥曲线中的证明、定值、定点问题(讲)-2022年高考数学二轮复习讲练测(新教材·新高考地区专用)(已下线)收官卷04--备战2022年高考数学一轮复习收官卷(新高考地区专用)(已下线)专题7 圆锥曲线之极点与极线 微点2 极点与极线问题常见模型总结福建省福州第一中学2022届高三上学期开学质检考试数学试题(已下线)专题41 定比点差法、齐次化、极点极线问题、蝴蝶问题北京市朝阳区2023届高三一模数学试题查漏补缺练习 (2)北京市中关村中学2024届高三上学期9月开学考试数学试题(已下线)重难点突破18 定比点差法、齐次化、极点极线问题、蝴蝶问题(四大题型)(已下线)专题18 圆锥曲线高频压轴解答题(16大题型)(练习)
6 . 已知椭圆
的左、右焦点分别为
,
,过
且与
轴垂直的直线交椭圆于点
,直线
与
轴的交点为
.
(1)求椭圆的离心率;
(2)过点
且斜率不为0的直线
交椭圆于
、
点,线段
的中点为点
,求证:直线
的斜率与直线
的斜率的乘积为定值.
![](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/a3fb78c5f885034612c0e030b920143d.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/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc3eab870388e522d5ab2cd30911f6b.png)
(1)求椭圆的离心率;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/9f0009063fe00277645aff1be6e32471.png)
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名校
解题方法
7 . 在平面直角坐标系
中,已知圆
,椭圆
,
为椭圆的右顶点,过原点
且异于坐标轴的直线与椭圆
交于
两点,直线
与圆
的另一个交点为
,直线
与圆
的另一个交为
,设直线
的斜率分别为
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b04d5596-2849-4cb7-8008-351c313a01a1.png?resizew=200)
(1)求椭圆的离心率;
(2)求
的值;
(3)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61f89c4a7e5d264bba22794a9a1403c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7da8ae0b0b96535db96d4f1a07243b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/60ef95894ceebaf236170e8832dcf7e3.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/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b04d5596-2849-4cb7-8008-351c313a01a1.png?resizew=200)
(1)求椭圆的离心率;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bba9be15b2def55c1dd9d54d0629b5.png)
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2021-08-26更新
|
488次组卷
|
2卷引用:浙江省嘉兴市第五高级中学2018-2019学年高二下学期期中数学试题
解题方法
8 . 已知点
和椭圆
.
(1)设椭圆的两个焦点分别为
,试求
的周长及椭圆的离心率;
(2)若直线
与椭圆
交于两个不同的点
,设直线
与
的斜率分别为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677b1e953bfbedbc5e390e87c5a1be71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
(1)设椭圆的两个焦点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f731b9b32af52fa59ac34047e900fc67.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
您最近一年使用:0次
2022-04-24更新
|
310次组卷
|
2卷引用:天津市红桥区2016-2017学年高三上学期期末理科数学试题
名校
解题方法
9 . 已知直线
经过椭圆
的左顶点A和上顶点D,设椭圆C的右顶点为B .
(1)求椭圆C的标准方程和离心率e的值;
(2)设点S是椭圆上位于x轴上方的动点,求证:直线AS与BS的斜率的乘积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18feaed4f3dd7698210ba302c81dca6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd72321801f7ce55ed0330289dd7c577.png)
(1)求椭圆C的标准方程和离心率e的值;
(2)设点S是椭圆上位于x轴上方的动点,求证:直线AS与BS的斜率的乘积为定值.
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名校
10 . 在平面直角坐标系xOy中,已知椭圆C:
的左、右顶点为A,B,右焦点为F.过点A且斜率为k(
)的直线交椭圆C于另一点P.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/9a46bba0-6b6f-4f68-afe4-a53f85f59b2f.png?resizew=195)
(1)求椭圆C的离心率;
(2)若
,求
的值;
(3)设直线l:
,延长AP交直线l于点Q,线段BQ的中点为E,求证:点B关于直线EF的对称点在直线PF上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104843b063a8882a2e12f357017a04b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/9a46bba0-6b6f-4f68-afe4-a53f85f59b2f.png?resizew=195)
(1)求椭圆C的离心率;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a2a34b4317deffa40ba34e269c2b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9b01aa61b6e3bcdd5d8b123df190ab.png)
(3)设直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785d23266ed97ab07e7b7f4e609b8487.png)
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