名校
1 . 已知
,直线l:
,椭圆C:
的离心率
,过C的右焦点且与x轴垂直的直线与l交于点P,若
(k表示斜率,O为坐标原点),则实数m的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809df5cc0872909977635ddec06940e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e3157e52b7e8ae7cb71a79c7a6b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb805cdd8433785fe05be399b415bee5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 数学家称
为黄金比,记为ω.定义:若椭圆的短轴与长轴之比为黄金比ω,则称该椭圆为“黄金椭圆”.以椭圆中心为圆心,半焦距长为半径的圆称为焦点圆.若黄金椭圆”:
与它的焦点圆在第一象限的交点为Q,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
A.![]() | B.黄金椭圆离心率![]() |
C.设直线OQ的倾斜角为θ,则![]() | D.交点Q坐标为(b,ωb) |
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2021-05-07更新
|
1119次组卷
|
3卷引用:广东省广州中学2021-2022学年高二上学期期中数学试题
3 . 已知曲线
的方程为
,直线
:
与曲线
在第一象限交于点
.
(1)若曲线
是焦点在
轴上且离心率为
的椭圆,求
的值;
(2)若
,
时,直线
与曲线
相交于两点M,N,且
,求曲线
的方程;
(3)是否存在不全相等
,
,
满足
,且使得
成立.若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb35212fddffca72021a984cfb1eccea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff186a9842c2e005014f9a82b6bec57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46de5f5993e7dcd0e828081045e502af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb35212fddffca72021a984cfb1eccea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3822d5b5db72c2560aa385bf6500fc47.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffff36f925d527a0000d36420ca864e1.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/192a35f0603f57bcc6ec1e75927ba916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(3)是否存在不全相等
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061baa765d2939a416300de14c45b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944f333c07f1ace36046b6069ce79b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68c35a19691406a91a5dec7e92e670a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
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2022-12-16更新
|
571次组卷
|
3卷引用:上海市格致中学2022-2023学年高二下学期第二次测试数学试题
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4 . 椭圆与正方形是常见的几何图形,具有对称美感,受到设计师的青睐.现有一工艺品,其图案如图所示:基本图形由正方形和内嵌其中的“斜椭圆”组成(“斜椭圆”和正方形的四边各恰有一个公共点).在平面直角坐标系
中,将标准椭圆绕着对称中心旋转一定角度,即得“斜椭圆”
,则“斜椭圆”的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea330dc8af514feddb053850ea3cdf3.png)
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2023-10-17更新
|
243次组卷
|
3卷引用:海南省儋州市洋浦中学2023-2024学年高二上学期期中数学试题(B卷)
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5 . 在对表面为曲面的工件进行磨削时应当选用尺寸适当的圆形砂轮,如果砂轮半径太大,则磨削时工件与砂轮接触处附近的那部分会磨去太多.现有一工件,其截面内表面是一长轴长为4,离心率为
的椭圆,在对其内表面进行抛光时,所选用砂轮的半径最大为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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6 . 已知椭圆
的两个焦点坐标分别为
,离心率为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0586ffe4bc516265086c6b5eafd1eed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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7 . 已知直线
与椭圆
:
交于
两点,弦
平行
轴,交
轴于
,
的延长线交椭圆于
,下列说法正确的个数是( )
①椭圆
的离心率为
;
②
;
③
;
④以
为直径的圆过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/8a726e4d-1875-444a-b3ce-9dc9ca9dd4fd.png?resizew=206)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8481f8c148f7ee6e0ee000d38ea62ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
①椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5020a41ba83aa373e56279a8da9fb82f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68736e6fe6530d1b4bd4e8e9885de2a.png)
④以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/8a726e4d-1875-444a-b3ce-9dc9ca9dd4fd.png?resizew=206)
A.1个 | B.2个 | C.3个 | D.4个 |
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2022-11-24更新
|
523次组卷
|
3卷引用:四川省德阳市德阳市第五中学2022-2023学年高二上学期期中数学(理)试题
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8 . 已知首项为正数的等比数列
的公比为
,曲线
,则下列叙述正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a990fa001792799459b7289c35da50.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.![]() |
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2022-02-02更新
|
546次组卷
|
3卷引用:江苏省南通市海安市实验中学2022-2023学年高二上学期期中数学试题
解题方法
9 . 已知正方体
的棱长为4,
是侧面
内任一点,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/28/8711b5c7-ecf6-42c2-a5cc-4d1c66c0efce.png?resizew=166)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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10 . 在等腰梯形
中,
,且
,以下选项正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133034c577f86cd876302fd20102c990.png)
A.![]() |
B.等腰梯形![]() ![]() |
C.若双曲线以![]() ![]() ![]() |
D.若椭圆以![]() ![]() ![]() |
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