1 . 椭圆
的焦点
的坐标为_____ ,若
为椭圆上任意一点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53836c455d2f63d7ad643dcead96e00.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89c03d164b45b7e9d3426efa62eb33a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48932773034bb6e1651acf140d47822c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53836c455d2f63d7ad643dcead96e00.png)
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名校
2 . 如图曲线AB是以O为对称中心的椭圆的四分之一,A,B分别为长、短轴端点; 现只用圆规确定该椭圆的右焦点位置,步骤:以____ 为圆心以______ 为半径画弧与x轴的交点.(填序号即可)①点O;② 点A;③点B;④ OB长;⑤ OA长.
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3 . 如图,我们把由半椭圆
:
和半椭圆
:
合成的曲线称作“果圆”.
,
是曲线
的焦点,
是曲线
的焦点,则
的周长为______ .过
且斜率为
的直线
交曲线
于
两点,则
=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b15fd3defc2234d9c822f740fdec6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95dde2ac65923a484c9bbda2fc274aee.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69559cc63085775fd0802997db15c751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2401bc9c26cc3b0b8384c7139bd58fff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/04357ba2-c881-469a-bcdb-b2499b4340cf.png?resizew=165)
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4 . 椭圆
上的点到焦点的距离最大值为________ ,一个圆经过该椭圆的三个顶点,且圆心在
轴的正半轴上,则该圆的标准方程为________________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
5 . 椭圆
上一点P到右焦点F的距离为3,则P到左焦点的距离是______ ,顶点在原点的抛物线C的焦点也为F,则其标准方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
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22-23高二·江苏·假期作业
6 . 若椭圆
的焦点在y轴上,且长轴长是短轴长的2倍,则m的值为________ ,焦点坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cd26242a98977b5be7dfd4fcf9f2d1.png)
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22-23高二·江苏·假期作业
解题方法
7 . 设F1,F2是椭圆
的焦点,则焦距为________ ;若P为椭圆上一点,则
的周长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
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8 . 如图,我们把由半椭圆
和半椭圆
合成的曲线称作“果圆”.
,
,
是相应半椭圆的焦点,则
的周长为______ ,直线
与“果圆”交于
,
两点,且
中点为
,点
的轨迹方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8393d2b1a354dfc2a0eed1a7acbb26ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a88b650d4e92afc358076df9868798.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/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69559cc63085775fd0802997db15c751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ff39dd1dfc9caf911ad0d11ba21d66.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/227e2618-528a-436f-be1d-107136427014.png?resizew=137)
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2023-04-14更新
|
469次组卷
|
4卷引用:山东省德州市2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 已知直线
与
轴的交点为
,与
轴的交点为
.
(1)将直线
绕着点
按逆时针方向旋转45°得到直线
,则直线
的斜率为___________ .
(2)若
、
是椭圆
的一个焦点和一个顶点,
是椭圆的另一个焦点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cd9525965cb26975f038270226817c.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb31826e94cde6199ed7f93139f3e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)将直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cd9525965cb26975f038270226817c.png)
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10 . 焦点在
轴上的椭圆
的离心率为
,则
的值为______ ;焦距为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caaad72a682e8a673e5bf3544a500ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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