解题方法
1 . 在平面直角坐标系
中,动圆C经过定点
,且与定直线l:
相切.
(1)求动圆圆心C的轨迹方程;
(2)经过点F的直线与动圆圆心C的轨迹分别相交于A,B两点,点P在直线l上且BP∥x轴,求证:直线AP经过原点O.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
(1)求动圆圆心C的轨迹方程;
(2)经过点F的直线与动圆圆心C的轨迹分别相交于A,B两点,点P在直线l上且BP∥x轴,求证:直线AP经过原点O.
您最近一年使用:0次
2 . 已知抛物线
.
(1)设
为抛物线
上横坐标为1的定点,
为圆
上的上的动点,若抛物线
与圆
无公共点,且
的最小值
,求
的值;
(2)设直线
交抛物线
于
,
两点,另一条直线
交抛物线
于
,
两点,
交
于点
,且直线
,
的斜率均存在,
(
为坐标原点),四边形
的四条边所在直线都存在斜率,直线
的斜率不等于0,求证:
(
,
分别为直线
,
的斜率)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbb6cbf601c8d08db363827baefc296.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8908cf4b3f2538e7b3d99e06705aac2f.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/7ab884b4fd41f26f2482ea49a6e62c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c258c53a14590047273bf849d5713e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4356a596535d4e905ae47e191940f34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4846c3da6f0078204c4b3ac6d3de074f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7496bc74d5f35d405b3debed173afb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1dc007e36c78ab98df4cd2383b4c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fd7f8d00aac0c708cf0909d688ddfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
名校
3 . 已知动圆
过点
,并与直线
相切.
(1)求动圆圆心
的轨迹方程
;
(2)已知点
,过点
的直线
交曲线
于点
,设直线
的斜率分别为
,求证:
为定值,并求出此定值.
![](https://img.xkw.com/dksih/QBM/2019/2/2/2132192816668672/2133485308272640/STEM/6addb7941c974eed80d6e73ae9453532.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca5a1d8622bf1e983867c8bbe6bb9f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948438fafb06683f7ca427b677e778a7.png)
您最近一年使用:0次
2018-05-24更新
|
1448次组卷
|
3卷引用:【全国市级联考 】江西省南昌市2018届高三第三次文科数学模拟试题
解题方法
4 . 已知抛物线
的焦点F,点
在抛物线C上.
(1)求
;
(2)过点M向x轴作垂线,垂足为N,过点N的直线l与抛物线C交于A,B两点,证明:
(O为坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8aed33984ccc91282d8a1c2be27cd0.png)
(2)过点M向x轴作垂线,垂足为N,过点N的直线l与抛物线C交于A,B两点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
您最近一年使用:0次
解题方法
5 . 已知点
,直线
,
为
轴右侧或
轴上动点,且点
到
的距离比线段
的长度大1,记点
的轨迹为
.
(1)求曲线
的方程;
(2)设点
在曲线
上,
,
为曲线
上异于点
的两个动点,且直线
,
的斜率互为相反数,求证:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f32ef32dfc25c0432e5be48d2e7c372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
6 . 如图所示,已知点
是抛物线
上一定点,直线
的倾斜角互补,且与抛物线另交于
,
两个不同的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/80984a12-c5be-4d0c-bdff-f177a3aa5f92.png?resizew=172)
(1)求点
到其准线的距离;
(2)求证:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35863acd3e2ad4e5eb056952b9e25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1bd115fa8e48e214fd2b90b0df6a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/80984a12-c5be-4d0c-bdff-f177a3aa5f92.png?resizew=172)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2019-11-12更新
|
1001次组卷
|
4卷引用:江西省南昌市东湖区第十中学2019-2020学年高二上学期期中数学试题
7 . 已知抛物线
的焦点为
,
为
上一点且纵坐标为4,
轴于点
,且
.
(1)求
的值;
(2)已知点
,
是抛物线
上不同的两点,且满足
.证明:直线
恒过定点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfba66e25f01d30e190e1458375da661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adb5ea2e5533717253ff00a6ecdf562.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3757244698d32aab7a9af1e044bf1da9.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/da006b1390397b520a0e8767cd49e7f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e1ce520d999c067d9301e0de4a7c15.png)
您最近一年使用:0次
名校
解题方法
8 . 已知抛物线
,焦点为F,准线为l,线段OF的中点为G.点P是C上在x轴上方的一点,且点P到l的距离等于它到原点O的距离.
(1)求P点的坐标.
(2)过点
作一条斜率为正数的直线
与抛物线C从左向右依次交于A,B两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
(1)求P点的坐标.
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14dd75003428d5b4071aabbaa4d11cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c443f5fc06491a7f1fdd470467cc5581.png)
您最近一年使用:0次
名校
解题方法
9 . 已知过抛物线
的焦点F的直线交抛物线于
,
两点,求证:
(1)
为定值;
(2)
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c62fe38f14f20e968c5b7122552cdc.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
10 . 在平面直角坐标系
中,已知圆心为点
的动圆恒过点
,且与直线
相切,设动圆的圆心
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过
轴上点
的直线
与
相切于点
,过
且垂直于
的直线交
于
两点,
为线段
的中点,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12afb7d94cc8c3aa927930fc328839c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次