1 . 已知抛物线
,过焦点的直线
与抛物线
交于两点A,
,当直线
的倾斜角为
时,
.
(1)求抛物线
的标准方程和准线方程;
(2)记
为坐标原点,直线
分别与直线
,
交于点
,
,求证:以
为直径的圆过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82796f5bb05438453a1e06a4fa83d6a1.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.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)
您最近一年使用:0次
2023-09-23更新
|
1186次组卷
|
8卷引用:贵州省黔西南州部分学校2024届高三上学期9月高考适应性月考(一)数学试题
贵州省黔西南州部分学校2024届高三上学期9月高考适应性月考(一)数学试题贵州省贵阳第一中学2024届高三上学期高考适应性月考数学试题(已下线)专题突破卷23 圆锥曲线大题归类广东省揭阳市揭西县2023-2024学年高二上学期期末数学试题(已下线)第三章 圆锥曲线的方程(压轴题专练)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(C卷)湖北省部分学校2024届高三下学期模拟考试数学试题吉林省延边市第二中学2023-2024学年高二上学期期中考试数学试卷
名校
2 . 在圆锥
中,已知高
,底面圆的半径为4,
为母线
的中点;根据圆锥曲线的定义,下列四个图中的截面边界曲线分别为圆、椭圆、双曲线及抛物线,下面四个命题,正确的个数为
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/f1161492-c1c7-4cf4-be85-be3776112d5a.png?resizew=559)
①圆的面积为
;
②椭圆的长轴为
;
③双曲线两渐近线的夹角正切值为
④抛物线中焦点到准线的距离为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/f1161492-c1c7-4cf4-be85-be3776112d5a.png?resizew=559)
①圆的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9609625b502348556ff8ba32deac8caa.png)
②椭圆的长轴为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb1f865738e0be47387e19392dd7cbe.png)
③双曲线两渐近线的夹角正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
④抛物线中焦点到准线的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98ee8ce2c56dccae6b63b5a9ca022b8.png)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
2019-04-04更新
|
2305次组卷
|
6卷引用:【全国百强校】上海市闵行区七宝中学2019届高三第二学期3月月考数学试题
【全国百强校】上海市闵行区七宝中学2019届高三第二学期3月月考数学试题(已下线)重难点05 空间向量与立体几何-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)重难点06 解析几何-2021年高考数学【热点·重点·难点】专练(上海专用)福建省莆田第十五中学2019届高三二模数学(理)试题2019年河北省衡水市高三二模数学(理)试题(已下线)数学(上海卷)
解题方法
3 . 已知点A是抛物线
的对称轴与准线的交点,点B为抛物线的焦点,P在抛物线上且满足
,当
取最大值时,点P恰好在以
、
为焦点的双曲线上,则双曲线的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bcdcd019945933d20cc6e90af7eb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 已知抛物线
上一点
到焦点
的距离
,倾斜角为
的直线经过焦点
,且与抛物线交于两点
、
.
(1)求抛物线的标准方程及准线方程;
(2)若
为锐角,作线段
的中垂线
交
轴于点
.证明:
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ddd8188218c214b934c35564f87673c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9e89f5ece16db5cf7c5f4fdc56ec1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671b66ae9432d2220c49e5d1da9a6984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求抛物线的标准方程及准线方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285a703081e781113a77f3b221011a72.png)
您最近一年使用:0次
2019-09-13更新
|
940次组卷
|
4卷引用:【全国市级联考 】四川省内江市2018-2019学年高二下学期期末检测数学(理)试题
名校
解题方法
5 . 已知
分别为椭圆
:
的上.下焦点,
是抛物线
:
的焦点,点
是
与
在第二象限的交点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de6ec9dd0c64ca7dfd76f342b75b7f0.png)
(1)求椭圆
的标准方程;
(2)与圆
相切的直线
:
(其中
)交椭圆
于点
,若椭圆
上一点
满足
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb223b8777ab973970491bf0dcc6806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/0de6ec9dd0c64ca7dfd76f342b75b7f0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e717059f6e5395d9883195d3f85b0d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd730237d9754f078f8c2df62a50c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c9e94b312670b9b0f2fa9f3889a676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476c2f32ae7f47f91b00aafccde79a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7043c5176a2673360277467c88198e1.png)
您最近一年使用:0次
6 . 已知抛物线
上一点
到焦点F的距离
,倾斜角为α的直线经过焦点F,且与抛物线交于两点A、B.
(1)求抛物线的标准方程及准线方程;
(2)若α为锐角,作线段AB的中垂线m交x轴于点P.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eda0d8732b07b06693bde233fb208c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3294a1b0769d2936880580b991b870a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90e4d97e31ea11615f23e53c285b319.png)
(1)求抛物线的标准方程及准线方程;
(2)若α为锐角,作线段AB的中垂线m交x轴于点P.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3a52a11565502a8d918d493604f425.png)
您最近一年使用:0次