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1 . 已知一个装有半瓶水的圆柱形玻璃杯,其底面半径为
,玻璃杯高为
(玻璃厚度忽略不计),其倾斜状态的正视图如图所示,
表示水平桌面.当玻璃杯倾斜时,瓶内水面为椭圆形,阴影部分
为瓶内水的正视图.设
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68f35b8432dad8fad85309c42f4d2f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fa622aae9a94f518967806eaec9544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70732cfd9e5e332e0fc1c1575a7ab2d.png)
A.当![]() ![]() |
B.当椭圆的离心率最大时,![]() |
C.当椭圆的焦距为4时,![]() |
D.当![]() |
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2 . 设椭圆C:
的左、右顶点和椭圆
的左、右焦点均为E,F.P是C上的一个动点(异于E,F),已知直线EP交直线
于点A,直线FP交直线
于点B.直线AB与椭圆
交于点M,N,O为坐标原点.
(1)若b为定值,证明:
为定值;
(2)若直线OM,ON的斜率之积恒为
,求b.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8c4b0e11e5894346b27e4656336c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e7a9b887d3dca1953a4f271d7b60a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f09e84f509537abd3dfaa20d7915675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee023dde0cd66b17a3ec5775d4b7d714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)若b为定值,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0ba14e41e306e5633ad4bf1cdedd8.png)
(2)若直线OM,ON的斜率之积恒为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
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3 . 在平面直角坐标系xOy中,长、短轴所在直线不与坐标轴重合的椭圆称为“斜椭圆”,将焦点在坐标轴上的椭圆绕着对称中心顺时针旋转
,即得“斜椭圆”
,设
在
上,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315082c24416a968957e7f4905526c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.“斜椭圆”的焦点所在直线的方程为![]() | B.![]() ![]() |
C.旋转前的椭圆标准方程为![]() | D.![]() |
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4 . 已知椭圆
的离心率为
分别是G的左、右顶点,F是G的右焦点.
(1)求m的值及点
的坐标;
(2)设P是椭圆G上异于顶点的动点,点Q在直线
上,且
,直线
与x轴交于点M.比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c39d8227c3f373e6dae8e46fd410f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a16354f17e5e6c9943cc721d63f830f.png)
(1)求m的值及点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)设P是椭圆G上异于顶点的动点,点Q在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a3b3ab26376be3df144adc6ec6bbea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea2c1df63a599a774043f6c3b881ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30c8db27f13442553eacf2b144a75ec.png)
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5 . 已知椭圆
:
,直线
:
交椭圆于M,N两点,T为椭圆的右顶点,
的内切圆为圆Q.
(1)求椭圆
的焦点坐标;
(2)求圆Q的方程;
(3)设点
,过P作圆Q的两条切线分别交椭圆C于点A,B,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b801e3da6f1b42d1f68cbf88cbfb4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf66a5f30d94390f59c6a3d1ae6c46.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求圆Q的方程;
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cc4e8043fb27abccf766c5f314dfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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解题方法
6 . 已知椭圆的焦点是椭圆
的顶点,椭圆
的焦点也是
的顶点.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654317ca05d25fee978869723ba8d0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/937c5db73d81da5525d4d35885dac04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
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2023·全国·模拟预测
解题方法
7 . 已知曲线
为焦点在x轴上的椭圆,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee27917c0aa38f9dbbb619d01f1cc4d8.png)
A.![]() | B.![]() ![]() |
C.m的值越小,C的焦距越大 | D.![]() ![]() |
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2022·全国·模拟预测
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8 . 如图所示,平面直角坐标系
中,四边形
满足
,
,
,若点
,
分别为椭圆
:
(
)的上、下顶点,点
在椭圆
上,点
不在椭圆
上,则椭圆
的焦距为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd99a6862833b220a7371852a3570bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2f21563f519fc8c47288b2b020e63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d0d12d0e06969e58f56899ea3cd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171b08c1122ed5d395dc72e9a8ee1390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/3630d768-f176-4123-8f79-2f6d1f90d5b0.png?resizew=137)
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2022-12-05更新
|
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5卷引用:2023年普通高等学校招生全国统一考试数学领航卷(六)
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9 . 曲线C的方程为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aae56504cfd74e294a012e4ffa91262.png)
A.存在实数![]() |
B.存在实数![]() |
C.存在实数![]() |
D.无论![]() ![]() ![]() |
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2022-05-25更新
|
2335次组卷
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7卷引用:重庆市第八中学校2022届高考全真模拟数学试题
重庆市第八中学校2022届高考全真模拟数学试题圆锥曲线之间的综合问题(已下线)专题39 双曲线及其性质-1(已下线)考向32 椭圆(重点)(已下线)第17讲 双曲线10大基础题型总结(1)(已下线)专题3.17 圆锥曲线的方程全章综合测试卷-基础篇-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)第12讲 双曲线(5大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
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解题方法
10 . 一个平面α斜截一个足够高的圆柱,与圆柱侧面相交的图形为椭圆E.若圆柱底面圆半径为r,平面α与圆柱底面所成的锐二面角大小为θ
,则下列对椭圆E的描述中,正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/2/7/2911129391480832/2938269518077952/STEM/2e56f41f-4ed2-4b9c-bd32-7a1e7ee5ba49.png?resizew=106)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d342f40541f8c90c95a63a98c9743cc.png)
![](https://img.xkw.com/dksih/QBM/2022/2/7/2911129391480832/2938269518077952/STEM/2e56f41f-4ed2-4b9c-bd32-7a1e7ee5ba49.png?resizew=106)
A.短轴为2r,且与θ大小无关 | B.离心率为cos θ,且与r大小无关 |
C.焦距为2r tan θ | D.面积为![]() |
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2022-03-17更新
|
757次组卷
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3卷引用: 吉林省长春市实验中学2022-2023学年高三下学期模拟考试(五)数学试题