名校
解题方法
1 . 小明同学某天发现,在阳光下的照射下,篮球在地面留下的影子如图所示,设过篮球的中心
且与太阳平行光线垂直的平面为
,地面所在平面为
,篮球与地面的切点为
,球心为
,球心
在地面的影子为点
;已知太阳光线与地面的夹角为
;
(1)求平面
与平面
所成角
(用
表示);
(2)如图,
为球
的一条直径,
为
在地面的影子,点
在线段
上,小明经过研究资料发现,当
时,篮球的影子为一椭圆,且点
为椭圆的焦点,线段
为椭圆的长轴,求此时该椭圆的离心率(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/b9fe09cf-3e20-4cbc-a31d-aa10d41cf688.png?resizew=169)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/66a61df9-8468-4831-9f9c-9b2891cf417f.png?resizew=168)
(1)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77993759b8615ef0b42cb56ef027ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb9fe45c7d4dd213d9c640150daec06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
名校
2 . 画法几何的创始人——法国数学家蒙日发现:在椭圆
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
中,任意两条互相垂直的切线的交点都在同一个圆上,它的圆心是椭圆的中心,半径等于长、短半轴平方和的算术平方根,这个圆就称为椭圆
的蒙日圆,其圆方程为
.已知椭圆
的离心率为
,点
均在椭圆
上,直线
:
,则下列描述正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968896e5a0785ec60382a3cb3cfcf260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b41ec44a7551e6561e27381313be50c.png)
A.点![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-11-22更新
|
532次组卷
|
2卷引用:浙江省A9协作体2023-2024学年高二上学期期中联考数学试题
名校
解题方法
3 . 已知焦点分别在
轴上的两个椭圆
,且椭圆
经过椭圆
的两个顶点与两个焦点,设椭圆
的离心率分别是
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2023-11-19更新
|
1318次组卷
|
5卷引用:浙江省七彩阳光新高考研究联盟2023-2024学年高二上学期11月期中联考数学试题
浙江省七彩阳光新高考研究联盟2023-2024学年高二上学期11月期中联考数学试题河北省邯郸市永年区第二中学2023-2024学年高二上学期12月月考数学试题(已下线)模块三 专题3 小题满分挑战练(1) 期末终极研习室(高二人教A版)(已下线)专题03 圆锥曲线方程(3)江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一
名校
解题方法
4 . 下列说法不正确的是( )
A.椭圆![]() ![]() |
B.双曲线![]() ![]() |
C.存在过点![]() ![]() ![]() ![]() ![]() ![]() |
D.顶点在原点,对称轴是坐标轴,并且经过点![]() |
您最近一年使用:0次
解题方法
5 . 已知椭圆
,离心率为
,右焦点为
,抛物线
的焦点
到其准线的距离为1.
(1)求
的标准方程;
(2)若过
作斜率为
的直线交椭圆
于
,交
轴于
的中垂线交
轴于
,记以弦
为直径的圆
的面积为
的面积为
,求
.
(3)已知
且
,若斜率为
的直线与椭圆
相交于
两点,且
中点
恰在抛物线
上.记
的横坐标为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e275781f32aab921e98996d1abc0a464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017a2e5f9e3d34edb75deddc570f4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b441ed4dff87bad469619581eedce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5d226450493c2710775806fb9e2363.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a11b8baa52b0907ec8638530f1a388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7a78a662576f9fd20b2568f44ca165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
您最近一年使用:0次
名校
6 . 有以下三条轨迹:
①已知圆
,圆
,动圆P与圆A内切,与圆B外切,动圆圆心P的运动轨迹记为
;
②已知点A,B分别是x,y轴上的动点,O是坐标原点,满足
,AB,AO的中点分别为M,N,MN的中点为P,点P的运动轨迹记为
;
③已知
,点P满足PA,PB的斜率之积为
,点P的运动轨迹记为
.设曲线
的离心率分别是
,则( )
①已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4af322ade58a465ffb4deecd0ee8b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3a2b5033a60426bebc34dfd3d631f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
②已知点A,B分别是x,y轴上的动点,O是坐标原点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179d7920ec6cd22f3a0cfa6738260153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cfaecde50d789695cc6b98e3a41316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d86ab7c97cd8a0b15ba5efc1be94230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a809ca7fdd64561639655b464bdbc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5916c998f2252c850c78851abc0e29dc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-02-17更新
|
554次组卷
|
3卷引用:浙江省金华十校2022-2023学年高二上学期期末数学试题
名校
7 . 如图,已知椭圆
和双曲线
具有相同的焦点
,
,A、B、C、D是它们的公共点,且都在圆
上,直线AB与x轴交于点P,直线CP与双曲线
交于点Q,记直线AC、AQ的斜率分别为
、
,若椭圆
的离心率为
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26edd7d076460e7aa7e8f319cb2be370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
A.2 | B.![]() | C.3 | D.4 |
您最近一年使用:0次
2023-02-13更新
|
1858次组卷
|
3卷引用:浙江省宁波市鄞州中学2023-2024学年高二上学期11月月考数学试题
名校
解题方法
8 . 已知椭圆
:
,椭圆
与椭圆
的离心率相等,并且椭圆
的短轴端点就是椭圆
的长轴端点,据此类推:对任意的
且
,椭圆
与椭圆
的离心率相等,并且椭圆
的短轴端点就是椭圆
的长轴端点,由此得到一个椭圆列:
,
,
,
,则椭圆
的焦距等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a2d3cd8e283ae9d04bee5ab2e0895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17841281fb2e0e3170bb51898bee079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17841281fb2e0e3170bb51898bee079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a2d3cd8e283ae9d04bee5ab2e0895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a2d3cd8e283ae9d04bee5ab2e0895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080d73fe94ee5fe5f34505d900cedede.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-02-03更新
|
462次组卷
|
5卷引用:浙江省温州市2022-2023学年高二上学期期末数学试题(A卷)
浙江省温州市2022-2023学年高二上学期期末数学试题(A卷)浙江省温州市2022-2023学年高二上学期期末数学试题(B卷)新疆乌鲁木齐市第101中学2022-2023学年高二下学期开学考试数学试题(已下线)模块四 专题4 重组综合练(浙江)期末终极研习室(高二人教A版)湖北省黄石市部分学校2023-2024学年高二上学期期末联考数学试卷
解题方法
9 . 已知椭圆
和双曲线
具有相同的焦点,离心率分别为
,椭圆的长轴恰好被双曲线的焦点、顶点、中心平分为若干条等长线段,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-01-12更新
|
553次组卷
|
2卷引用:浙江省宁波市九校2022-2023学年高二上学期期末联考数学试题
名校
解题方法
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![]() ![]() ![]() |
您最近一年使用:0次