2024高三下·全国·专题练习
1 . 关于曲线
有以下五个结论:
①当
时,曲线C表示圆心为
,半径为
的圆;
②当
,
时,过点
向曲线C作切线,切点为A,B,则直线AB的方程为
;
③当
,
时,过点
向曲线C作切线,则切线方程为
;
④当
时,曲线C表示圆心在直线
上的圆系,且这些圆的公切线方程为
或
;
⑤当
,
时,直线
与曲线C表示的圆相离.
以上正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983416abb2a19329feee784025961f1a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484121f8076509e579f91dd919e4632a.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4681073487d89441a8db549f4187dda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e729c58c343ef3cebb8bd720278c26ed.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d694b4de9f0bef15f2917a4ed214e01c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9891da64b7a4a2f83f2af4d4c313246e.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e8c8fd6d9c4ed8cf35504db1918b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a10732055a4228ab2b1a0f1bb16b67.png)
⑤当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1578a4b2d61c2b65532f5dcb25003.png)
以上正确结论的序号为
您最近一年使用:0次
2 . 过点P
作圆
的切线
,求切线
的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66791c865401dc5f480e277eae870941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
3 . 如图,在平面直角坐标系
中,过
上的点
作切线
,
分别与直线
,
交于点
,圆
与
轴交于点
.
(1)若
点坐标是
,求直线
的方程;
(2)若
是圆
上的动点,证明:两条动直线
的交点
总在同一个椭圆
上,并求出椭圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a327470311e876d8489eeb8c66435dc4.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf2917e77945b30da7be9b48b0b317a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9454e7762d6924d4a9e5dcf31fb6bc74.png)
![](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/cf639890f27a42e1383cc6cfa14117a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d55806ac-c399-4b9c-b012-1d4e5c5bbf3a.png?resizew=180)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceff0e7d103475c3ba9a2712f373185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7040823265da65a030f0c81f3ae7ddd0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37254351125380127823c0fd7d95458d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7040823265da65a030f0c81f3ae7ddd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2024-02-23更新
|
93次组卷
|
2卷引用:中原名校2022年高三上学期第一次精英联赛文科数学试题
4 . 如图,已知点
和圆
.
(1)求以
为直径的圆N的标准方程;
(2)设圆M与圆N相交于A,B两点,试判断直线
是否为圆M的切线.若是,请求出直线
和
的方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a4848c9764b738e58d6efbc0b9cf77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c3adf33b6fbd524c3e85e04b125fb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/5fcf3e0e-4665-464d-a22d-052072e14796.png?resizew=148)
(1)求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(2)设圆M与圆N相交于A,B两点,试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
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5 . 圆
在点
处的切线方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dccc5720967ee3edce0174255e8ed8.png)
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名校
6 . 已知圆
.
(1)过点
作圆
的切线,求切线的方程;
(2)若直线
过点
,且被圆
截得的弦长为2,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e133eb3bb45bc93ecc88a186d7be937b.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5a6145990adf5574f0e0f2fc828ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e94852797399ba119b090fa957ee3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
7 . 直线
与双曲线
的两条渐近线交于
两点,
分别为双曲线的左、右焦点.
(1)求过点
的圆的方程;
(2)设(1)中的圆和双曲线在第一象限交于点
,求圆在点
处的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7638c88f01d609d79947033ed4ff36a2.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea98501007b43f9e3253d4ae91a1ae9.png)
(2)设(1)中的圆和双曲线在第一象限交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-02-18更新
|
92次组卷
|
2卷引用:山东省菏泽市2023-2024学年高二上学期期末教学质量检测数学试题
解题方法
8 . 已知抛物线
和圆
,若抛物线与圆在交点处的切线互相垂直,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c649a1c8fa9d55613723d80d3f4833b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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解题方法
9 . 已知椭圆C:
(
)的离心率为
,直线l:
是椭圆C与圆
:
的一条公切线.
(1)求椭圆C的方程;
(2)若点
为椭圆C的一点,直线
:
交圆
于M,N两点,以M,N为切点分别作圆
的切线,两条切线交于点Q,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15839b3af175b63e496dbf320ca7d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆C的方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c8d4762cddd87ca1baa79e0d1e158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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解题方法
10 . 已知圆
的方程是
,
(1)若点
为圆
上一点,过点M作圆
的切线,求该切线方程.
(2)若点
为圆
外一点,过点M作圆
的两条切线,切点分别为A、B,
①求直线AB的方程.
②若
为直线
上的一个动点,试讨论直线AB是否恒过定点,若是,求出定点坐标;若不是,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①求直线AB的方程.
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f049d6f117b0ab3459ae444350dd66be.png)
您最近一年使用:0次