1 . 如图,点
为抛物线
上位于第一象限的一点,F为抛物线焦点,满足
.
(1)求抛物线C的方程;
(2)点M为直线
上的动点,H为点E关于x轴的对称点,连接
、
分别交C于点A、B,连接
交直线l于点N.
①求证:直线
过定点;
②求证:以
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32dd0829b0b8c2ff6f0229a1333dbc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ceb1c169f659ef1ef183c8c65b9daff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/4a29ec81-6b43-46f6-8cdb-2c769160b79b.png?resizew=170)
(1)求抛物线C的方程;
(2)点M为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②求证:以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2 . 已知抛物线
是该抛物线上两点,
为坐标原点,
为焦点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc5ca1d1efb220bd5cc8f4b1e3554d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
A.若直线![]() ![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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3 . 已知抛物线
:
的焦点为
,直线
过焦点
分别交抛物线
于点
、
、
、
,其中
位于
轴同侧,且
经过点
,记
,
的斜率分别为
,
,则下列正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc39f01920227d524b789061274db4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d281a5c8b38326678e1c99e5f975b9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e12d4e98345c00e7daf3168eeeb1ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88920aab87278ca982c235e13f847c4e.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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4 . 已知F为抛物线
的焦点,点A,B在该抛物线上且位于x轴的两侧,
(其中O为坐标原点),则
与
面积之和的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725958ac97752a7b37a679ce16bcfe91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7959e0af6500a4756c8a50ad8638be61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fff07a5663bcc25319bfa6876706f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618a5b77f4a4b83d8c144e7a180e12f3.png)
A.![]() | B.3 | C.![]() | D.![]() |
您最近一年使用:0次
2022-10-17更新
|
1935次组卷
|
8卷引用:浙江省杭州学军中学2022-2023学年高二上学期期中模拟数学试题
22-23高二上·浙江·期末
名校
解题方法
5 . 设点
为抛物线
:
(
)的动点,
是抛物线的焦点,当
时,
.
(1)求抛物线
的方程;
(2)当
在第一象限且
时,过
作斜率为
,
的两条直线
,
,分别交抛物线于点
,
,且
,证明:直线
恒过定点,并求该定点的坐标;
(3)是否存在定圆
:
,使得过曲线
上任意一点
作圆
的两条切线,与曲线
交于另外两点
,
时,总有直线
也与圆
相切?若存在,求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6196f68aa254e0bc1061551d47bb934c.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5603d29560e66b2293cea1e3b02289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a690a05dc243e3c6736a6de514106ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)是否存在定圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46cdaa65fa93e3e3d332a31d8650fc79.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-09-29更新
|
694次组卷
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4卷引用:高中数学 高二上-8
名校
解题方法
6 . 已知抛物线
, 点
是抛物线
上的点.
(1)求抛物线的方程及
的值;
(2)直线
与抛物线交于
两点,
,且
,求
的最小值并证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188026eaa20f137d70e994415c8b32d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求抛物线的方程及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1325c6fe42a9e5c04520d8a9bb6821b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79891395ddbe2b31f3c91523176f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4c0b1d1e4abf9057893bcd09e5940a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09821e8bfe3d8560cc814d3e210bbb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-11-23更新
|
485次组卷
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4卷引用:浙江省台州市玉环市玉城中学2021-2022学年高二上学期期中数学试题
7 . 已知抛物线
上点
到焦点
的距离为4.
(1)求
,
的值;
(2)如图所示,设A、
是抛物线上分别位于
轴两侧的两个动点,且
(其中
为坐标原点).
(ⅰ)求证:直线
必过定点,并求出该定点
的坐标;
(ⅱ)过点
作
的垂线与抛物线交于
、
两点,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb1a15498d7a4910a26ae500591df63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)如图所示,设A、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abdcc3d02baa36a2d2ffc5106719a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(ⅰ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ⅱ)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/9bcfe377-3a48-4914-bd83-a069fae2155e.png?resizew=161)
您最近一年使用:0次
2016-12-03更新
|
854次组卷
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3卷引用:浙江省台州市三门启超中学2021-2022学年高二上学期期末质量评估试卷A数学试题