1 . 设抛物线
的焦点为
,
是
上的一个动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.点![]() ![]() ![]() |
B.点![]() ![]() ![]() |
C.以![]() ![]() |
D.记点![]() ![]() ![]() ![]() |
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|
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2卷引用:海南省儋州市2023-2024学年高二下学期期末考试数学试题
名校
解题方法
2 . 已知点
,直线
,动圆过点F且与直线l相切,动圆圆心轨迹为曲线
.
(1)求曲线
的方程;
(2)已知定点
,过点P的直线m交曲线C与M,N两点.
①若直线
与直线l交于点H,求
的最小值;
②在y轴上是否存在与点P不同的定点Q,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42502a5730e1930d77d7100d1e34707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0d26df529bbd8953f127102885f54e.png)
②在y轴上是否存在与点P不同的定点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28390341f43e405f91454b05e2f406d1.png)
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3 . 已知F为抛物线
的焦点,M,N,P,Q是C上四个不同的动点,满足直线
,
过F,其中M,P在第一象限,若直线
与x轴的交点为
,
,
,
,
的面积分别为
,
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90be0db8c2f6610ee002461f45cdab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322b7fc53308233b59dce017d044c3e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f426b792991048b55d4cfaddb6ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7b3c1d0057c4b0405f28b48043d9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce74b3d06976675398a88cee8064fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
A.![]() ![]() | B.直线![]() ![]() |
C.![]() | D.![]() |
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2卷引用:江西省部分重点中学2023-2024学年高二上学期期末联考数学试题(A卷)
名校
解题方法
4 . 已知
、
,点
为曲线
上动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3326927e4b01e981a19109633141e06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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3卷引用:黑龙江省哈尔滨市第一二二中学校2023-2024学年高二下学期3月月考数学试题
5 . 已知
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f7aca9642b54b10fe660fcf89891e0.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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6 .
为坐标原点,以
为准线,
为焦点的抛物线
的方程为:
.过
的直线交
于
两点,
于
于
为线段
的中点.下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e627296086a74b6bec2c13f48ce3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcd0a07c239333bc9245de3b833043b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e71abd446a59195761c7b1684d73dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5889e1f093f2c35273d3132ef8434e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
A.![]() ![]() |
B.![]() |
C.直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() |
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7 . 已知抛物线C:
,直线l:
与C交于
,
两点,O为坐标原点,P是直线
上任意一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d0aafd52e26c241c46d0206f42f415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
8 . 已知圆的方程
,
,
,抛物线过
两点,且以圆的切线为准线.
(1)求抛物线焦点的轨迹C的方程;
(2)已知
, 设x轴上一定点
, 过T的直线交轨迹C于
两点(直线
与
轴不重合),求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求抛物线焦点的轨迹C的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c153027427477bcd0a7228b14ce96cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf5077ae09443a75fb8301841116a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b800af3d8614f3f30eefa7de8d0b581f.png)
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|
900次组卷
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3卷引用:四川省成都市2023-2024学年高二上学期期末校级调研联考数学试题
2023·全国·模拟预测
9 . “心形线”体现了数学之美,某研究小组用函数图象:
,
和抛物线
的部分图象围成了一个封闭的“心形线”,过
焦点
的直线
交
(包含边界点)于
,
两点,
是
或
上的动点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd7dee9c935065ab38edeca954614aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f2851cc5488a103e508c12e904becf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa019b9a83ddada0aee6a01a97e6fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/0560b96f-b8f5-4785-a751-7ba321c36c8f.png?resizew=153)
A.抛物线![]() ![]() |
B.![]() |
C.![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
10 . 如图,已知点
是棱长为2的正方体
的底面
内(包含边界)一个动点,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/9bb9554b-1d03-41ed-a909-00ec63dc5c3e.png?resizew=159)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/9bb9554b-1d03-41ed-a909-00ec63dc5c3e.png?resizew=159)
A.过![]() ![]() ![]() |
B.当点![]() ![]() ![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次