1 . 在平面直角坐标系
中,圆
外的点
在
轴的右侧运动,且
到圆
上的点的最小距离等于它到
轴的距离,记
的轨迹为
.
(1)求
的方程;
(2)过点
的直线交
于
,
两点,以
为直径的圆
与平行于
轴的直线相切于点
,线段
交
于点
,证明:
是
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b2ffdcc66148aedaa575dde03d144e.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
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解题方法
2 . 在平面直角坐标系xOy中,抛物线E:
上一点
到焦点F的距离
.不经过点S的直线l与E交于A,B.
(1)求抛物线E的标准方程;
(2)若直线AS,BS的斜率之和为2,证明:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146ea2d6699971783e857f46f79357d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0b22964c9f8629905d8e5d1d3a0953.png)
(1)求抛物线E的标准方程;
(2)若直线AS,BS的斜率之和为2,证明:直线l过定点.
您最近一年使用:0次
2022-03-09更新
|
731次组卷
|
12卷引用:“星云”2022届高三上学期第二次线上联考数学试题
“星云”2022届高三上学期第二次线上联考数学试题河北省唐山市第一中学2021-2022学年高二上学期期中数学试题(已下线)考向42 抛物线山西省太原市第五中学2021-2022学年高二上学期12月月考数学试题(已下线)第十一章 圆锥曲线专练18—抛物线综合练习2-2022届高三数学一轮复习(已下线)一轮复习大题专练68—抛物线2(定点问题1)—2022届高三数学一轮复习江西省重点中学盟校2022届高三第一次联考数学(理)试题(已下线)热点11 圆锥曲线的定义方程与性质【热点·重点·难点】专练(全国通用)河南省豫北名校2021-2022学年高二下学期4月份教学质量检测理科数学试题西藏拉萨中学2021-2022学年高二3月月考数学(理)试题西藏拉萨中学2021-2022学年高二3月月考数学(文)试题河南省开封市天成学校2023届高三文科数学试题
21-22高二·全国·课后作业
3 . 若抛物线
(
)上一点M到它准线的距离为2,且点M到此抛物线顶点的距离等于点M到它的焦点的距离,求此抛物线的焦点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
您最近一年使用:0次
解题方法
4 . 已知抛物线
上的点
到其焦点F的距离为5.
(1)求C的方程;
(2)过点
的直线l交C于A,B两点,且N为线段
的中点,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3efcbe144dc3afc7ff3862f8df96a8.png)
(1)求C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6f0ed8eb1f519ac067f35099237459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
5 . 已知抛物线
的焦点是椭圆
的右焦点,且两条曲线的一个交点为
,若E到
的准线的距离为
,到
的两焦点的距离之和为4.
(1)求椭圆
的方程;
(2)过椭圆
的右顶点的两条直线
,
分别与抛物线
相交于点A,C,点B,D,且
,M是AC的中点,N是BD的中点,证明:直线MN恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d624a18acd4fccfedaf984862adc004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cdcc25290844c9d4c088bf58afada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72096b73b7d2a2ceccd0ae6d7f91f1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa585b9257ed0798213a9ae9b87d291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
您最近一年使用:0次
2022-01-27更新
|
513次组卷
|
2卷引用:河南省原阳县第─高级中学等2021-2022学年高三上学期模拟测试数学(理科) 试题
解题方法
6 . 已知抛物线
的准线与圆
相切.
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898626103771136/2903349987270656/STEM/cb57bac1-13c9-4258-ad0b-29077c08d28b.png?resizew=164)
(1)求
;
(2)若定点
,
,M是抛物线上的一个动点,设直线AM,BM与抛物线的另一交点分别为
、
恒过一个定点.求出这个定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898626103771136/2903349987270656/STEM/cb57bac1-13c9-4258-ad0b-29077c08d28b.png?resizew=164)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)若定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18e9b80fdeaa8bd3cf97b3c214448f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee07d86765c4fb74ac647742f16bd57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92cd947a7803ff4cb438685130eee95.png)
您最近一年使用:0次
7 . 在平面直角坐标系
中,已知抛物线
的焦点
与椭圆
的右焦点重合
(1)求椭圆
的离心率;
(2)求抛物线
的方程;
(3)设
是抛物线
上一点,且
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9802ceacc6f6b67b3a91ea759d2c6ab.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)设
![](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/1f3cf3c6570184ef6c9e0500bf178d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
解题方法
8 . 在平面直角坐标系xOy中,动点P到点
的距离比到直线
的距离小2.
(1)求动点P的轨迹方程;
(2)记动点P的轨迹为曲线C,过点F的直线1与曲线C交于A,B两点,点M是x轴上异于点F的一点,点F到直线AM的距离为
,点F到直线BM的距离为
.是否存在一点M、使得
恒成立?若存在,求出点M的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14436636ec6a7aec09cb63cecf6e970d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7e51699bcf9d57cc560edded62d3ec.png)
(1)求动点P的轨迹方程;
(2)记动点P的轨迹为曲线C,过点F的直线1与曲线C交于A,B两点,点M是x轴上异于点F的一点,点F到直线AM的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc82280a60309e03d58340025a43cff.png)
您最近一年使用:0次
9 . 已知抛物线C:
上一点
与焦点F的距离为
.
(1)求
和p的值;
(2)直线l:
与C相交于A,B两点,求直线AM,BM的斜率之积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7585c7944d095b903c6e0d3dcbc228e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139e6e6c81a5c5f7179d855e0e977769.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
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解题方法
10 . 已知点F为抛物线
:
(
)的焦点,点
在抛物线
上且在x轴上方,
.
(1)求抛物线
的方程;
(2)已知直线
与曲线
交于A,B两点(点A,B与点P不重合),直线PA与x轴、y轴分别交于C、D两点,直线PB与x轴、y轴分别交于M、N两点,当四边形CDMN的面积最小时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ec5921ec65f6ce31284cea043910e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30ee8b98bd071f65863897db9cbacb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a0328dde917c3e6d0f1ca9ddb6027b.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51698f7095e795d4f0527b986ac1db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
您最近一年使用:0次
2022-01-22更新
|
727次组卷
|
2卷引用:山东省烟台市2021-2022学年高二上学期期末数学试题