解题方法
1 . 已知抛物线
的准线
,直线
与抛物线
交于
,
两点,
为线段
的中点,则下列说法中正确的为_________________ .(填写所有正确说法的序号)
①若
,则以
为直径的圆与
相交;
②若
,则
(
为坐标原点);
③过点
,
分别作抛物线
的切线
,
,若
,
交于点
,则
;
④若
,则点
到直线
的距离大于等于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8603a175d1a7685208f64d4a4e8521ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48054662c2d9b0dca46f5ae482cef509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e28cb80a0d7ea39bc8f3b6b90fac5c.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b36445a8b9102f748e24aeca52838ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4244af644b011d8292c8533368a9c9a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
③过点
![](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/c5db41a1f31d6baee7c69990811edb9f.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/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/904b21bba351171abdc8482a906499d8.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753c43eb11c1f1e92ff392d3a989b95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6503ca085e3ca5f2ba723b0dd66e210b.png)
您最近一年使用:0次
解题方法
2 . 过抛物线
焦点
的直线与抛物线交于
两点,作
垂直抛物线的准线
于
,
为坐标原点,则下列结论正确的是_______ (填写序号).
①
;
②存在
,使得
成立;
③
;
④准线
上任意点
,都使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a8528cd0649f5a271a37f88ba532ba.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb35b2338cb644c9cc0000094ea63b23.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e902c3982957249ce719e9af7b98d292.png)
④准线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f387a4813c2ab2880cf66d768196c70.png)
您最近一年使用:0次
名校
解题方法
3 . 贝塞尔曲线是计算机图形学和相关领域中重要的参数曲线.法国数学象卡斯特利奥对贝塞尔曲线进行了图形化应用的测试,提出了De Casteljau算法:已知三个定点,根据对应的比例,使用递推画法,可以画出地物线.反之,已知抛物线上三点的切线,也有相应成比例的结论.如图所示,抛物线
,其中
为一给定的实数.
(1)写出抛物线
的焦点坐标及准线方程;
(2)若直线
与抛物线只有一个公共点,求实数k的值;
(3)如图,A,B,C是H上不同的三点,过三点的三条切线分别两两交于点D,E,F,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6402365aeb523fd88a62ae002f8ba2bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/5/a6dbe941-0041-450a-a826-342bdb7bad16.png?resizew=189)
(1)写出抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f82accad6edb09040f343941ed14a2a.png)
(3)如图,A,B,C是H上不同的三点,过三点的三条切线分别两两交于点D,E,F,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a96cc64535a00a0ef8050d4f8ed7114.png)
您最近一年使用:0次