1 . 已知抛物线
的焦点为
,直线
与抛物线C交于A,B两点.
(1)求
的面积;
(2)过抛物线C上一点Р作圆
的两条斜率都存在的切线,分别与抛物线C交于异于点P的两点D,E.证明:直线DE与圆M相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
(2)过抛物线C上一点Р作圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095c9f730b1d8c5eff9de7024a3474b3.png)
您最近一年使用:0次
2021-05-07更新
|
609次组卷
|
3卷引用:安徽省马鞍山市2021届高三下学期第三次教学质量监测理科数学试题
解题方法
2 . 如图,已知点
,圆
:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/1a9042b7-b417-4817-b8b6-1427426abd0c.png?resizew=167)
(1)求过点
且与圆
相切的直线方程;
(2)设圆
与
轴的正半轴的交点是
,斜率为
的直线
过点
,且与圆
交于不同的两点
.
①设直线
的斜率分别是
,求证:
为定值;
②设
的中点为
,点
,当
,且
为整数时,求以
为直径的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497911bc462170183e81d95bd509b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/1a9042b7-b417-4817-b8b6-1427426abd0c.png?resizew=167)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
①设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ca520748c8b8d3878fb112a89ada7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f36374ce95a4945d0e58264c2b271f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f637d8983f1139258cd0742c60d833e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2021-01-09更新
|
196次组卷
|
3卷引用:安徽省合肥市肥东县高级中学2020-2021学年高三上学期第三次月考数学(理)试题
名校
解题方法
3 . 已知圆
,点P为椭圆
上一点,A,B分别是椭圆C的左右顶点.
(1)若过P点的直线与圆O切于点Q(Q位于第一象限),求使得
面积最大值时的直线PQ的方程;
(2)若直线AP,BP与y轴的交点分别为E,F,以EF为直径的圆与圆O交于点M,求证:直线PM平行于x轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
(1)若过P点的直线与圆O切于点Q(Q位于第一象限),求使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
(2)若直线AP,BP与y轴的交点分别为E,F,以EF为直径的圆与圆O交于点M,求证:直线PM平行于x轴.
您最近一年使用:0次
2020-08-14更新
|
293次组卷
|
3卷引用:安徽省合肥市第一中学2020届高三下学期最后一卷数学(理)试题
安徽省合肥市第一中学2020届高三下学期最后一卷数学(理)试题(已下线)专题2.6 直线与圆锥曲线的位置关系(B卷提升篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)专题2.7 平面解析几何(B卷提升篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)
名校
4 . 已知椭圆
的离心率为
,左、右焦点分别为
,且
,
⊙
与该椭圆有且只有一个公共点.
(1)求椭圆标准方程;
(2)过点
的直线与⊙
相切,且与椭圆相交于
两点,求证:
;
(3)过点
的直线
与⊙
相切,且与椭圆相交于
两点,试探究
的数量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9b3989176291d0411305c31f590ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2d4ff799e2f87b3786a04c83f63d5d.png)
⊙
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cf28ef033367a93ab80801df41c88f.png)
(1)求椭圆标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d603b2b163e44a464f88a384da3229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1b84446336cb832a0da3b3d9c4ae55.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d603b2b163e44a464f88a384da3229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7fa328f91b9efe3e9e785625616d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b694a0cf87ff75a60a72ece1580e845f.png)
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