解题方法
1 . 已知抛物线
经过椭圆
的两个焦点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/90a3be1e-8525-415e-82af-b72b7b9c0cda.png?resizew=173)
(1)求椭圆
的离心率;
(2)设
,又点
为
与
不在
轴上的两个交点,若
的重心在抛物线
上,求
和
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ee03b5f5c40c4a64e15bd90673783e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2cfc8743c915f45bdccca70ab16648.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/90a3be1e-8525-415e-82af-b72b7b9c0cda.png?resizew=173)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208f32acf0666fcc867c56e41e0e7562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0023c9e8e0fec24d3aa77d09b2e4e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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解题方法
2 . 设抛物线
的准线与
轴交于
,焦点为
,以
、
为焦点,离心率
的椭圆与抛物线的一个交点为
,自
引直线交抛物线于
、
两个不同的点,点
关于
轴的对称点记为
,设
.
(1)求抛物线的方程和椭圆的方程;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478560c0e58cd542c0d9cdf3d049b8ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4694df7bd84ce284f10c6f7b284faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b3bf0867eaad259f29391e75eb63bb.png)
(1)求抛物线的方程和椭圆的方程;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddec8b37824ab314ad78991d659abd5.png)
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名校
解题方法
3 . 一个动圆与定圆
:
相内切,且与定直线
相切,则此动圆的圆心M的轨迹方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed65024898bb517e8cd6a2c663b836e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2977eea43a781e06d93e04a395a309.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-22更新
|
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2卷引用:宁夏石嘴山市第三中学2016-2017学年高二上学期第二次月考数学(理)试题
4 . 已知双曲线
的右焦点恰好是抛物线
的焦点
,且
为抛物线的准线与x轴的交点,N为抛物线上的一点,且满足
,则点
到直线
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06117c33dbfbc009d6a2509659315f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.![]() | B.1 | C.![]() | D.2 |
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2023-11-22更新
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6卷引用:【全国校级联考】滨海新区七所重点学校2018届高三毕业班联考数学(理)试题
【全国校级联考】滨海新区七所重点学校2018届高三毕业班联考数学(理)试题天津市滨海新区七所重点学校2017-2018学年高三毕业班联考数学(理)试题天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷4(已下线)专题03 圆锥曲线方程(2)(已下线)2.4.1 抛物线的标准方程(十四大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)第4讲: 圆锥曲线几何性质【练】
5 . 已知抛物线
的焦点为F,准线
与y轴的交点为M,动点A(异于原点O)在抛物线C上,当
与y轴垂直时,
.
(1)求抛物线C的方程;
(2)若直线
与抛物线C交于另一点B,证明:直线
的斜率与直线
的斜率互为相反数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ba3a6326dc83632fa772c1d34cbff9.png)
(1)求抛物线C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
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2卷引用:陕西省延安市延安新区2020-2021学年高二上学期学生发展水平调研检测(期末)理科数学试题
2020高三·江苏·专题练习
解题方法
6 . 点
到抛物线
的准线的距离为6,那么抛物线的标准方程是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e15e9463940aba61072e91e49b94f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf210c8c9e83e70f2d3ede1e18a5f3d.png)
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解题方法
7 . 如图,开口向右的抛物线对称轴与x轴重合,焦点位于坐标原点处,并且过点
.设直线
与抛物线交于
两点,直线
看与抛物线交于
两点.
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169711929909248/3169843440074752/STEM/cdb8ea8fb97149f8848f61456cc00bd0.png?resizew=317)
(1)求抛物线方程.
(2)求证:
.
(3)设直线
分别与y轴交于P,Q两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc756fb11c7c96bf318b5fae4982f507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47aca422a33ec9b9430d204659ff9fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c345dfe2ac9387357be143c0b96de6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756f66428eba953d4610f59a3479d143.png)
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169711929909248/3169843440074752/STEM/cdb8ea8fb97149f8848f61456cc00bd0.png?resizew=317)
(1)求抛物线方程.
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d298273d6dc5a07cc6f819ac3e63730.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15abfafc59b6f9f01f3be4db4df797d.png)
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8 . 已知抛物线
上一点
到其焦点的距离为5,双曲线
的右顶点为A,若双曲线的一条渐近线与直线
平行,则正实数
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bb0657a539d2f0f61afa44d502e120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f498ba6218eb7f5f5ca03cf9011b6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6卷引用:2015届湖北省黄冈市高三上学期元月调研考试文科数学试卷
解题方法
9 . 已知
是双曲线
的左、右焦点,拋物线
的准线过点
,若
为抛物线上一点,且
在
轴上方,
,则直线
的方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5de403dabee36d6ae22acc9df4fab3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
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解题方法
10 . 已知抛物线
的焦点F位于直线
上.
(1)求抛物线方程;
(2)过抛物线的焦点F作倾斜角为
的直线,交抛物线于A,B两点,求AB的中点C到抛物线准线的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(1)求抛物线方程;
(2)过抛物线的焦点F作倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
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