名校
1 . 已知抛物线C:y2=2px(p>0)的焦点F,直线y=4与y轴的交点为P,与抛物线C的交点为Q,且|QF|=2|PQ|.
(1)求p的值;
(2)已知点T(t,-2)为C上一点,M,N是C上异于点T的两点,且满足直线TM和直线TN的斜率之和为
,证明直线MN恒过定点,并求出定点的坐标.
(1)求p的值;
(2)已知点T(t,-2)为C上一点,M,N是C上异于点T的两点,且满足直线TM和直线TN的斜率之和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f476931aaa390e9d7c6d86d9a23224fd.png)
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名校
2 . 在平面直角坐标系
中,已知
是抛物线
上一点.
(1)若
到抛物线焦点
的距离为
,求点
的坐标;
(2)若
,过
的直线
交抛物线与另一点
,当
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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3 . 已知抛物线C; y2 =2x的焦点为F,准线为l, P为抛物线C上异于顶点的动点.
(1)过点P作准线1的垂线,垂足为H,若△PHF与△POF的面积之比为2:1,求点P的坐标;
(2)过点M(
,0)任作一条直线 m与抛物线C交于不同的两点A, B.若两直线PA, PB 斜率之和为2,求点P的坐标.
(1)过点P作准线1的垂线,垂足为H,若△PHF与△POF的面积之比为2:1,求点P的坐标;
(2)过点M(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
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2012·江苏南京·一模
解题方法
4 . 在综合实践活动中,因制作一个工艺品的需要,某小组设计了如图所示的一个门(该图为轴对称图形),其中矩形
的三边
、
、
由长6分米的材料弯折而成,
边的长为
分米 (
);曲线
拟从以下两种曲线中选择一种:曲线
是一段余弦曲线(在如图所示的平面直角坐标系中,其解析式为
),此时记门的最高点
到
边的距离为
;曲线
是一段抛物线,其焦点到准线的距离为
,此时记门的最高点
到
边的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/13/58200f66-ab68-477e-8354-fd33c5c41611.png?resizew=122)
(1)试分别求出函数
、
的表达式;
(2)要使得点
到
边的距离最大,应选用哪一种曲线?此时,最大值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dffc8f00c4e34f8113ba86977c3136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35bdb064cf560727bc3a161fa6a7e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf006d9cf9568dd567c25fd20a0c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9355c5cacc696e0cbcb68361e1c392b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e056a4bbf30ff67162a239543af932c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4700efcb84c4027ce7a50af0d5212fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e873e78a362bfe21fd2e2ed311e283.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/13/58200f66-ab68-477e-8354-fd33c5c41611.png?resizew=122)
(1)试分别求出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e056a4bbf30ff67162a239543af932c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e873e78a362bfe21fd2e2ed311e283.png)
(2)要使得点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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