1 . 已知抛物线
的焦点为
点
在
上. 若
到直线
的距离为4,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cc141e9b6050eae77c22dd46fd4ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5c664aa79a88c035d7ece15220a4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1c76111ee604ba947ad94a13695a2e.png)
A.7 | B.6 | C.5 | D.4 |
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2 . 已知抛物线
的焦点为F,P是C上一点,线段PF的中点为
.
(1)求C的方程;
(2)若
,O为原点,点M,N在C上,且直线OM,ON的斜率之积为2024,求证:直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8543a9925dffcc9c0c0e13cff19732a2.png)
(1)求C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83f589bf62f30ff300637d3cd71aef.png)
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3 . 已知抛物线C:
与椭圆E:
的一个交点为
,且E的离心率
.
(1)求抛物线C和椭圆E的方程;
(2)过点A作两条互相垂直的直线AP,AQ,与C的另一交点分别为P,Q,求证:直线PQ过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求抛物线C和椭圆E的方程;
(2)过点A作两条互相垂直的直线AP,AQ,与C的另一交点分别为P,Q,求证:直线PQ过定点.
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4 . 已知
为坐标原点,点
在抛物线
上,过点
的直线交
于
,
两点,则下列命题正确的是________ .
(1)
的准线为
;(2)直线
与
相切;(3)
;(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd4b5f5dfdca309903e5e3d1121d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f96ddb6b56f9ce7268b62cbc1a748d.png)
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5 . 已知抛物线
的焦点为
,过抛物线
上一点
作两条斜率之和为0的直线,与
的另外两个交点分别为
(均在
点下方),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.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/5f54dd475ff1321041c80738b201c3b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() ![]() |
B.若圆![]() ![]() ![]() ![]() ![]() |
C.直线![]() ![]() |
D.![]() ![]() |
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6 . 已知抛物线C:
的焦点为F,点
,N是抛物线C上一点,当
取得最小值时,
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261104a7c308433a0c0508ff20ea29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356547c08d2cd7ba5a6aaf412266d7b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1622b71bf051bfd14c79b2c75eca58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
A.7 | B.5 | C.![]() | D.![]() |
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7 . 已知抛物线C的顶点为原点,焦点F在x轴的正半轴,F到直线
的距离为
.点
为此抛物线上的一点,
.
(1)求抛物线方程和N点坐标;
(2)已知A、B是抛物线C上的两个动点,且点A在第一象限,点B在第四象限,直线
分别过点A、B且与抛物线C相切,P为
的交点.设C、D为直线
与直线
的交点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7116071164cdc45f5d312a437c68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c9ca0f54b6a84bb93d435933aae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715426331815c4e34ad97a8b66ab3ddd.png)
(1)求抛物线方程和N点坐标;
(2)已知A、B是抛物线C上的两个动点,且点A在第一象限,点B在第四象限,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
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8 . 已知
轴上一定点
,和抛物线
上的一动点
,若
恒成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba61ef91e5827a569ec11a681efa809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f29793c6a1016226ce22347d39f88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知抛物线
的焦点为
,点
在该抛物线上,且
,则
到
轴的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590fa7c70bd0a95eb7179a39d2157f6.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/75c21d430a0c8c8abee1de7e46523233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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138次组卷
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2卷引用:河北省南宫市私立丰翼中学2023-2024学年高二下学期第三次月考(5月)数学试卷
名校
解题方法
10 . 已知抛物线
和
的焦点分别为
,动直线
与
交于
两点,与
交于
两点,其中
,且当
过点
时,
,则下列说法中正确的是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd002e4153239401cbe0d56ab1164b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e43bb9b3ff712aeea6a52cea9e25f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1459402f901edc7c3bd6993b15be2805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf328ef13181498b339a6c9b9af0eb0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910215944e29fcfe2d439b7191192cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6179bd1936944d2977cab330e0e351ca.png)
A.![]() ![]() | B.已知点![]() ![]() ![]() |
C.![]() | D.若![]() ![]() ![]() |
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