1 . 中心在原点的双曲线
的焦点在x轴上,且焦距为4,请从下面3个条件中选择1个补全条件,并完成后面问题:
①该曲线经过点
;
②该曲线的渐近线与圆
相切;
③点
在该双曲线上,
,
为该双曲线的左、右焦点,当点
的纵坐标为
时,以
,
为直径的圆经过点
.
(1)求双曲线C的标准方程;
(2)过定点
能否作直线
,使
与此双曲线相交于
两点,且
是弦
的中点?若存在,求出
的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①该曲线经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aab000962b3e21db0bd949eb7a0d6fc.png)
②该曲线的渐近线与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea31a691dd967aa83caf78e0a2e95d05.png)
③点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求双曲线C的标准方程;
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355dffb42861f3e297694f4be77c694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
2 . 某同学回忆一次大型考试中的一道填空题,题目要求判断一条给定直线与给定圆的位置关系,该同学表示,题中所给直线与圆的方程形式分别为
,
,但他忘记了方程中的三个参数的具体值,只记得
,并且他填写的结果为直线与圆相交.若数组
的每一种赋值的可能性都相等,则该同学该题答对的概率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8fa64fec535f51aacbae6480e744d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243e4c9ec9393f4aa3d64da6136b9e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6c9703877376f2469faef45141cc73.png)
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解题方法
3 . 下列说法:
①若
,则a的取值范围是
;
②若关于x方程
有两个不等实根,则k的取值范围是
;
③若x,y满足约束条件
,则
的取值范围为
;
④已知点
是圆
上的点,则
的取值范围是
;
⑤圆
上有4个点到直线
的距离为
.
其中正确的是______ .(只填写相应的序号 )
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa5b4a297839180fc3326eed4351bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b39f15729c7b85f666ce498fcd6203.png)
②若关于x方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66acde2de7a6b791b66c7d6264d9691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a2c9b2a4f6bb96f99461130f78c481.png)
③若x,y满足约束条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80d0871ab9d635e5cf36f4d0f3b7eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9f4c6be70f463b4422fedd4c981d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76156a5abf37c361f9287c0c4dc8396.png)
④已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab11ba6b230c4309e1b899eb58daae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b4814dceed7290bc3049b2620ccfc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2eedab1868828530de228aee6a714a.png)
⑤圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/730c71a1c8ccd9bd19ea075d6f38adb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac74fcec33998e08b909a3e52508791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
其中正确的是
您最近一年使用:0次
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4 . 求下列条件确定的圆的方程,并画出它们的图形:
(1)圆心为
,且与直线
相切;
(2)圆心在直线
上,半径为2,且与直线
相切;
(1)圆心为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4786edaf22bdc9d191becce18f836eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7691a78c7b2bb2f0a3ec82ce60a1cd09.png)
(2)圆心在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bbf68714436abcc9a8fdc01bd04895.png)
您最近一年使用:0次
2024-01-11更新
|
214次组卷
|
2卷引用:重庆市第七中学校2023-2024学年高二上学期期末模拟数学试题
解题方法
5 . 在直角坐标系
中,曲线
的参数方程为
,(
为参数,
).
(1)在平面直角坐标系
中,画出曲线
的图象;
(2)过定点
,斜率
的直线
与曲线
只有一个公共点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e824858b43372250cc404df221e708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34281318027f1d9d7cffd42d2cca8df.png)
(1)在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
6 . 已知两圆
,
.
(1)
和
的圆心分别为
和
,若直线
与线段
有交点,则实数
的取值范围是___________ .
(2)在一张画有直角坐标系的足够大的白纸上画出
和
,并将这两个圆的圆内部分均涂满红色,过原点画一条斜率为
的直线
,沿着
将该纸剪成两张纸,若这两张纸上红色部分的面积相等,则实数
取值的集合为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3482c9faf127d5248037bc7e036ed36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101db7e46ae221a40f0f36891faf3b20.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f49fc6babe4d5eba3b33891e75ec1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在一张画有直角坐标系的足够大的白纸上画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
7 . 求下列条件确定的圆的方程,并画出它们的图形:
(1)圆心为
,且与直线
相切;
(2)圆心在直线
上,半径为2,且与直线
相切;
(3)半径为
,且与直线
相切于点
.
(1)圆心为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2aaaeac424e47d4e8aa757677e944c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7691a78c7b2bb2f0a3ec82ce60a1cd09.png)
(2)圆心在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bbf68714436abcc9a8fdc01bd04895.png)
(3)半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb3e0b614f6571ee55c33ac08c9a4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f728cf9ce5311b6355148ec05e8e8cc.png)
您最近一年使用:0次
2021-02-06更新
|
980次组卷
|
4卷引用:人教A版(2019) 选择性必修第一册 新高考名师导学 第二章 2.5 直线与圆、圆与圆的位置关系