1 . 运用微积分的方法,可以推导得椭圆
(
)的面积为
.现学校附近停车场有一辆车,车上有一个长为
的储油罐,它的横截面外轮廓是一个椭圆,椭圆的长轴长为
,短轴长为
,则该储油罐的容积约为(
)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f64e8295d206562e50933dcecb8e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16738f0fce36cc80eb25d47597878527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70efab6d57221e9eee93200d045b0c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1188bdd135b8a2dc75f91e9839a1d3a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d553e4a26eb3012410ef7558a5fd6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:广东省深圳市龙华区2022-2023学年高二上学期期末数学试题
2 . 过双曲线C:
的左焦点
作直线l与双曲线C的右支交于点A,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565bc68d208cd5e0c90a32851faf3814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
A.双曲线C的渐近线方程为![]() |
B.点![]() |
C.直线l的斜率k取值范围是![]() |
D.若![]() ![]() |
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3 . 已知抛物线
.现将抛物线
绕原点顺时针旋转
,得到新抛物线
.记
的焦点为
.过点
的直线交抛物线
于
、
两点,若直线
的斜率为
,则下列关于
的说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12b5e5ff59f1eea47300d8d7ca9167e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.焦点![]() | B.![]() |
C.准线方程为![]() | D.![]() ![]() |
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4 . 下列命题为真命题的有( )
A.若![]() ![]() ![]() |
B.函数![]() ![]() |
C.“![]() ![]() |
D.当![]() ![]() |
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5 . 已知椭圆
和
,点
在
上,且直线
与
交于
、
两点,若点
在
上,使得
,则下列结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a87f5c5835dcc976ea0009d11ce07b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd7d594cd613385df149480dfbcefdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568efa7ae00715452edfec27d514e5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6daacbdd7db4c7c49a82072cf5e01ffe.png)
A.![]() ![]() | B.![]() |
C.直线![]() ![]() | D.四边形![]() ![]() |
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6 . 已知
是平面直角坐标系的原点,抛物线
的焦点为
两点在抛物线
上,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88eec86c17ca9025e2a6c7db421f5c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a063a96bd8db892d175d0a139541b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.若![]() ![]() ![]() |
B.直线![]() ![]() |
C.![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
7 . 在平面直角坐标系
中,已知点
在双曲线
的右支上运动,平行四边形
的顶点
,
分别在
的两条渐近线上,则下列结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc1bb67a4b30c947048ddf6a6471cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.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/c5db41a1f31d6baee7c69990811edb9f.png)
A.直线![]() ![]() ![]() | B.![]() |
C.![]() ![]() | D.四边形![]() ![]() |
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5卷引用:广东省深圳市南山区2023届高三上学期期末数学试题
广东省深圳市南山区2023届高三上学期期末数学试题辽宁省鞍山市普通高中2022-2023学年高二下学期第一次月考数学(A卷)试题辽宁省鞍山市2023届高三第二次质量监测数学试题(已下线)专题09 平面解析几何(已下线)湖北省“荆、荆、襄、宜四地七校”考试联盟2023-2024学年高二下学期期中联考数学试卷变式题6-10
8 . 点
是平面直角坐标系
上一动点,两直线
,
,已知
于点
,
位于第一象限;
于点
,
位于第四象限.若四边形
的面积为2.
(1)若动点
的轨迹为
,求
的方程.
(2)设
,过点
分别作直线
,
交
于点
,
.若
与
的倾斜角互补,证明直线
的斜率为一定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bce9bdeb6b4e2401d9907f4e3f0c540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc20ecfb48de46ccba10337431d7fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a92725a33c2e15a5ae19c6e0a563787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98cb0b951fb1a7f9fd49c00a5b23d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6c989fd224866658230526892e2bcb.png)
(1)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f27b9ed128f5ae9f16284228bf6fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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9 . 圆锥曲线具有丰富的光学性质,从椭圆的一个集点发出的光线,经过椭圆反射后,反射光线过椭圆的另一个焦点.如图,胶片电影放映机的聚光灯有一个反射镜.它的形状是旋转椭圆.为了使影片门(电影胶片通过的地方)处获得最强的光线,灯丝
,与影片门
应位于椭圆的两个焦点处.已知椭圆
:
,椭圆的左右焦点分别为
,
,一束光线从
发出,射向椭圆位于第一象限上的Р点后反射光线经过点
,且
,则
的角平分线所在直线方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54058d8ebebd0449a3f6a6bb8358ce3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/8bacf061-6f55-4ce7-8299-8520fab50df4.png?resizew=325)
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10 . 地震预警是指在破坏性地震发生以后,在某些区域可以利用“电磁波”抢在“地震波”之前发出避险警报信息,以减小相关预警区域的灾害损失.根据Rydelek和Pujol提出的双台子台阵方法,在一次地震发生后,通过两个地震台站的位置和其接收到的信息,可以把震中的位置限制在双曲线的一支上,这两个地震台站的位置就是该双曲线的两个焦点.在一次地震预警中,两地震台
站和
站相距
.根据它们收到的信息,可知震中到
站与震中到
站的距离之差为
.据此可以判断,震中到地震台
站的距离至少为( )
![](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/0f3fb33e7fb8709bd8d5db686644d50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57601db9d81fffe2b6b472db94c3c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:广东省揭阳市普宁市2023-2024学年高二上学期期末数学试题
广东省揭阳市普宁市2023-2024学年高二上学期期末数学试题北京市东城区2022-2023学年高二上学期期末考试数学试题北京市一零一中学2023届高三下学期统练数学试题(一)(已下线)第21讲 双曲线及其标准方程7种常见考法归类(2)