1 . 已知抛物线
的焦点为F,直线
与抛物线C相切于点P,过点P作抛物线C的割线PQ,割线PQ与抛物线C的另一交点为Q,A为PQ的中点.过A作y轴的垂线与y轴交于点H,与直线l相交于点N,M为线段AN的中点.
(1)求抛物线C的方程;
(2)求证:点M在抛物线C上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06553b7e77205d053c1981e9c050d579.png)
(1)求抛物线C的方程;
(2)求证:点M在抛物线C上.
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名校
2 . 已知
是抛物线
上一点,
为
的焦点.
(1)若
,
是
上的两点,证明:
,
,
依次成等比数列.
(2)若直线
与
交于
,
两点,且
,求线段
的垂直平分线在
轴上的截距.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266504a4bd910b292c74765dc9772f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fbb6cbf601c8d08db363827baefc296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20171b65c618928b3f93d5996374722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dfb134869d6058b3d97ed01658ade0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33b315a25c667233befb2a1d542eb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a052a4645628e5ba018f5e2f17c1138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4428dc4e1db8f04c28ba1a4e3b3d2bc9.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f514aac874d83740f54a9a717149d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fc2bcbded30ecb9441f8fb4c8773c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2019-04-15更新
|
682次组卷
|
12卷引用:【省级联考】甘肃、青海、宁夏2019届高三3月联考数学(理)试题
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解题方法
3 . 已知直线
经过抛物线
的焦点且与此抛物线交于
,
两点,
,直线
与抛物线
交于
,
两点在
轴的两侧.
(1)证明:
为定值;
(2)求直线
的斜率的取值范围;
(3)已知函数
在
(
)处取得最小值
,求线段
的中点
到点
的距离的最小值(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afc4ea76647ad29c250dfcc2f5e40dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e61e0a1bc2ab34fe0cd1de9f59b0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85af6eaff9a4e3e9af4e9c1f4f7b996.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b589e8bcefa5a24e72041b1325abb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fa55e2f154fced2fb1ee3411f0a53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac8fa800c00933279f2b20e5034438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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