解题方法
1 . 已知椭圆E:
的离心率为
,短轴长为4.
(1)求椭圆E的方程;
(2)设直线
与椭圆E交于C,D两点,在y轴上是否存在定点Q,使得对任意实数k,直线QC,QD的斜率乘积为定值?若存在,求出点Q的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆E的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c1f1adf71591678365c085c08fd61.png)
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2023-04-24更新
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4卷引用:陕西省宝鸡市2023届高三三模文科数学试题
名校
解题方法
2 . 已知椭圆C中心在原点O,焦点在x轴上,其长轴长为焦距的2倍,且过点
,F为其左焦点.
(1)求椭圆C的标准方程;
(2)过左焦点F的直线L与椭圆C交于A,B两点,当
时,求直线L的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67baac84cf5c95d06d50c36cab7c68.png)
(1)求椭圆C的标准方程;
(2)过左焦点F的直线L与椭圆C交于A,B两点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4762d6f54b7bfde2f996052dbbf9f6.png)
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解题方法
3 . 已知椭圆
的左,右顶点分别为
,上顶点M与左,右顶点连线
的斜率乘积为
,焦距为
.
(1)求椭圆
的方程;
(2)设过点
的直线
与椭圆C交于
两点,O为坐标原点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c6ba69264c8f203cd756581bc6280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ff9f648fedec284a11a9761cb6183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-02-17更新
|
279次组卷
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2卷引用:陕西省安康市2022-2023学年高二下学期开学摸底考试文科数学试题
解题方法
4 . 已知椭圆
过点
,短轴上一个端点到右焦点的距离为2.
(1)求椭圆C的标准方程;
(2)设过定点
的直线l与椭圆C交于不同的两点A,B,若坐标原点O在以线段AB为直径的圆外,求直线l的斜率k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆C的标准方程;
(2)设过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ed90ebf0061c8a79beed307fc1719a.png)
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2023-02-14更新
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159次组卷
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2卷引用:陕西省渭南市临渭区2022-2023学年高二上学期期末理科数学试题
5 . 已知椭圆
,
的三个顶点都在椭圆C上,且P为椭圆C的左顶点,直线AB经过点
.
(1)求
面积的最大值.
(2)若
三边所在的直线斜率都存在,且分别记为
,试判断
是否为定值.若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09ba15dae73d98a7d7d590fa55d139d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a43b04ee141752475f25e55ca96256.png)
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2023-02-06更新
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3卷引用:陕西省商洛市2022-2023学年高二上学期期末文科数学试题
6 . 已知椭圆
的右焦点为
,且离心率为
.
(1)求椭圆
的方程;
(2)若直线
与曲线
相切,与椭圆
交于
,
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4093faf6c3a57732776e53489ad1b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d9d951fbf8deaa373d6377dff3f6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0761e63cb3a4113d50f6bf808cdc031.png)
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解题方法
7 . 已知椭圆
的离心率为
,其左、右焦点分别为
,过
且垂直于
轴的直线被椭圆
所截得的线段长为3.
(1)求椭圆
的方程;
(2)直线
与椭圆
交于
两点,射线
交椭圆
于点
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4cdd2a4e98eeeed7f2e014d53af76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/91edc7e2d4811f5ea6c01284cf00393a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa841ce5d58b64f747a3c1b69bb20a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769116141926fb5948bee3d10201f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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2022-12-29更新
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2卷引用:陕西省部分学校2022-2023学年高三上学期12月大联考文科数学试题
名校
解题方法
8 . 已知椭圆
,倾斜角为
的直线过椭圆的左焦点
和上顶点B,且
(其中A为右顶点).
(1)求椭圆C的标准方程;
(2)若过点
的直线l与椭圆C交于不同的两点P,Q,且
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e2c8fa12344e36efba94ab6f6df05d.png)
(1)求椭圆C的标准方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d3175ab92b729dfd24f209e448e600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3de67f64270935ceb31a169d5c8a84.png)
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2022-12-17更新
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8卷引用:陕西省西安市铁一中学2023-2024学年高三上学期第二次月考理科数学试题
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9 . 已知椭圆
的离心率
,它的一个顶点
恰好是抛物线
的焦点.
(1)求椭圆
的方程;
(2)若直线
交椭圆
于不同的两点E,F,线段EF的中点为
,且E,F都在以
为圆心的圆上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e091bcc3593e18e1a771fcb2ffd42aff.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc1b5d8c4ef05d1a48bace1affe1e1c.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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10 . 已知椭圆
:
的离心率为
,椭圆
上的一点
到两焦点的距离之和等于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
(1)求椭圆
的方程;
(2)若直线
:
交椭圆
于不同的两点
,
,且
,
为坐标原点,求实数
的值
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627e3c988f71572a7da37bdff2317251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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