1 . 如图所示,已知抛物线
的焦点为F,过F的直线交抛物线于A,B两点,A在y轴左侧且AB的斜率大于0.
![](https://img.xkw.com/dksih/QBM/2021/11/3/2843403305623552/2845588730691584/STEM/db0f10f7-a5b3-4364-b57d-6ae6ea343fd4.png?resizew=354)
(1)当直线AB的斜率为1时,求弦长
的长;
(2)已知
为x轴上一点,弦AB过抛物线的焦点F,且斜率
,若直线PA,PB分别交抛物线于C、D两点,问是否存在实数
使得
,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://img.xkw.com/dksih/QBM/2021/11/3/2843403305623552/2845588730691584/STEM/db0f10f7-a5b3-4364-b57d-6ae6ea343fd4.png?resizew=354)
(1)当直线AB的斜率为1时,求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489b1787ca5f053dbd34c8dcfbcdba16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 已知抛物线
的焦点为F,直线l过点F且与C相交于A、B两点,当直线l的倾斜角为
时,
.
(1)求C的方程;
(2)若
的垂直平分线
与C相交于M、N两点,且A、M、B、N四点在同一圆上,求l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c348601813d70ba64ffca73cf2256f3.png)
(1)求C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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2020-11-13更新
|
256次组卷
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3卷引用:浙江省杭州市学军中学2020-2021学年高三上学期期中数学试题
名校
解题方法
3 . 已知抛物线
:
过点
,直线
经过抛物线的焦点
与抛物线交于
,
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/9c897a1a-0ad5-49d3-8716-09c55b8ffbfa.png?resizew=160)
(1)若直线
的方程为
,求
的值;
(2)若直线
,
的斜率为
,
,且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c1dfc3b8de8d7b6cfff140359b5f59.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/9c897a1a-0ad5-49d3-8716-09c55b8ffbfa.png?resizew=160)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.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/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . 如图,O为坐标原点,点F为抛物线C1:
的焦点,且抛物线C1上点M处的切线与圆C2:
相切于点Q.
(Ⅰ)当直线MQ的方程为
时,求抛物线C1的方程;
(Ⅱ)当正数p变化时,记S1 ,S2分别为△FMQ,△FOQ的面积,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eb771069a3bf8ce5777bbe07d040bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d22c4afd75d76767cbcbc59a3a2436.png)
(Ⅰ)当直线MQ的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7ca47ea8b78dd4c0389eee8620d523.png)
(Ⅱ)当正数p变化时,记S1 ,S2分别为△FMQ,△FOQ的面积,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f652af0a51b7f47fa50163158c53cf7.png)
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2017-06-04更新
|
1190次组卷
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8卷引用:【全国百强校】浙江省宁波市镇海中学2019届高三上学期期中考试数学试题