解题方法
1 . 已知椭圆
的右焦点为
,点
在椭圆上.
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771818496/STEM/ceda92aa65fa4f249e1c241c2a05df10.png?resizew=229)
(1)求椭圆的方程;
(2)点
在圆
上,且
在第一象限,过
作圆
的切线交椭圆于
两点,求证:
的周长是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327126f348c456f0c628a2f57648ecea.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470766108672/1572470771818496/STEM/ceda92aa65fa4f249e1c241c2a05df10.png?resizew=229)
(1)求椭圆的方程;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50667ce76318b23b69ac6b8e16dc80d0.png)
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2 . 已知曲线
:
,曲线
:
.曲线
的左顶点恰为曲线
的左焦点.
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182252675072/1572182258581504/STEM/2a9b1e37-94e6-4c4f-a140-338e45f9a385.png?resizew=170)
(Ⅰ)求
的值;
(Ⅱ)设
为曲线
上一点,过点
作直线交曲线
于
两点.直线
交曲线
于
两点.若
为
中点,
求证:直线
的方程为
;
求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ade220833dcafb0c48aabe0d88c28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f9d5c45a20f43a6d7709a23a6ff2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182252675072/1572182258581504/STEM/2a9b1e37-94e6-4c4f-a140-338e45f9a385.png?resizew=170)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d0d8d9e98a198d566c7ef90748eee4.png)
求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2016-12-03更新
|
1615次组卷
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2卷引用:2015届辽宁省沈阳市东北育才学校高三第八次模拟理科数学试卷
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名校
3 . 如图,圆
与
轴相切于点
,与
轴正半轴相交于
两点(点
在点
的下方),且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/9f1e1599-2835-4ff8-ad46-aed81e934d71.png?resizew=167)
(1)求圆
的方程;
(2)过点
任作一条直线与椭圆
相交于两点
,连接
,求证:
.
![](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/c6614916203fe0146d6797138da3db4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/cbc5931d25e50c27e61e78347f9370e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/9f1e1599-2835-4ff8-ad46-aed81e934d71.png?resizew=167)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729cf1d18cbb0ff509b51be7c445c34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5ce23462dfd28929430b74b9590940.png)
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21卷引用:2012届福建省福州市高三综合练习理科数学试卷
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11-12高三上·北京东城·期末
4 . 设A,B分别为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de4b2b286eef9210f677af0bfae04ae.png)
的左、右顶点,椭圆的长轴长为
,且点
在该椭圆上.
(1)求椭圆的方程;
(2)设
为直线
上不同于点
的任意一点,若直线
与椭圆相交于异于
的点
,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
为钝角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de4b2b286eef9210f677af0bfae04ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e684712aade8dcebb62716843791034.png)
(1)求椭圆的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d9d4662edaa19665d9890888f6e2e0.png)
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2016-11-30更新
|
790次组卷
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3卷引用:2011届北京市东城区高三上学期期末理科数学卷
2014·北京昌平·二模
5 . 已知椭圆
的左右焦点分别为
,点
为短轴的一个端点,
.
(1)求椭圆
的方程;
(2)如图,过右焦点
,且斜率为
的直线
与椭圆
相交于
两点,
为椭圆的右顶点,直线
分别交直线
于点
,线段
的中点为
,记直线
的斜率为
.
求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2f2d391b1e6304eb2bba560d0ccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b9ee165fff07f902ab60ee54fcb1f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e6558d22c2ab634a0929fcb75f4b97.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c471fc77430cf0c3a90f8513ebf68.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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26260c10afb34f543d86b67898134f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f90b1f89215b0f848d8b29542e51d0.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee1b62f7a91af431d9217079419fdf6.png)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571746933161984/1571746939027456/STEM/329afe870b754e469a7c10a2fb8d2715.png)
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2011·北京朝阳·一模
名校
6 . 已知
,
为椭圆
的左、右顶点,
为其右焦点,
是椭圆
上异于
,
的动点,且
面积的最大值为
.
(Ⅰ)求椭圆
的方程及离心率;
(Ⅱ)直线
与椭圆在点
处的切线交于点
,当直线
绕点
转动时,试判断以
为直径的圆与直线
的位置关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44095accc17467f9721ef46c879d8613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7406e11d72eaece13b00dd40b5c300b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
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2016-11-30更新
|
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6卷引用:2011届北京市朝阳区高三第一次综合练习数学理卷
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真题
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7 . 在平面直角坐标系xOy中,已知椭圆
.如图所示,斜率为k(k>0)且不过原点的直线l交椭圆C于A,B两点,线段AB的中点为E,射线OE交椭圆C于点G,交直线x=﹣3于点D(﹣3,m).
(1)求m2+k2的最小值;
(2)若|OG|2=|OD|∙|OE|,
(i)求证:直线l过定点;
(ii)试问点B,G能否关于x轴对称?若能,求出此时△ABG的外接圆方程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4d3fac09fb943b5da320395ff0879a.png)
(1)求m2+k2的最小值;
(2)若|OG|2=|OD|∙|OE|,
(i)求证:直线l过定点;
(ii)试问点B,G能否关于x轴对称?若能,求出此时△ABG的外接圆方程;若不能,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/489c2274-66e7-4655-aeeb-9a6b7820e184.png?resizew=218)
您最近一年使用:0次
2016-12-03更新
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3326次组卷
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4卷引用:2011年普通高等学校招生全国统一考试文科数学(山东卷)
2011年普通高等学校招生全国统一考试文科数学(山东卷)天津市静海县第一中学2017-2018学年高二上学期期末终结性检测数学(理)试题(附加题)(已下线)专题45 盘点圆锥曲线中的定点问题——备战2022年高考数学二轮复习常考点专题突破(已下线)第五篇 向量与几何 专题5 调和点列 微点3 调和点列(三)