名校
解题方法
1 . 已知双曲线E:
的左,右焦点分别为
,离心率为2,点B为
,直线
与圆
相切.
(1)求双曲线E方程;
(2)过
的直线l与双曲线E交于M,N两点,
①若
,求
的面积取值范围:
②若直线l的斜率为k,是否存在双曲线E上一点Q以及x轴上一点P,使四边形PMQN为菱形?若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad29801f799532ee7dda9658c30e373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb7edd919d58c85c4813f43729eb5af.png)
(1)求双曲线E方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096a1ef5efc86957efc9fbf5a24c50a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
②若直线l的斜率为k,是否存在双曲线E上一点Q以及x轴上一点P,使四边形PMQN为菱形?若存在,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986e3613290b456532843d5ad4c6e67.png)
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2 . 已知圆
与圆
相内切,则实数a的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c50969d52579a90d3367869ab55a2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
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2024-04-19更新
|
292次组卷
|
2卷引用:江苏省南京市南京师范大学附属中学2023-2024学年高二下学期期中考试数学试卷
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3 . 已知圆
:
,圆
:
交于
,
两点,
在第二象限,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
______ ;若过点
的弦交两圆于
,
,且
,则直线
的斜率是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018c3a123e449e364d16650411c23faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b86d31cbcf786f5b3e50f280d5c0ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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4 . 已知线段AB的端点B的坐标是
,端点A的运动轨迹是曲线C,线段AB的中点M的轨迹方程是
.
(1)求曲线C的方程;
(2)已知斜率为k的直线l与曲线C相交于两点E,F(异于原点O),直线OE,OF的斜率分别为
,且
,
①证明:直线l过定点P,并求出点P的坐标;
②若
,D为垂足,证明:存在定点Q,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d02dba7080b2d1e0d7a4a16a48a0d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d1ac5adb13362206cfc2f2fb624d30.png)
(1)求曲线C的方程;
(2)已知斜率为k的直线l与曲线C相交于两点E,F(异于原点O),直线OE,OF的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73849df3a825a25491e0e18f846d9904.png)
①证明:直线l过定点P,并求出点P的坐标;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8aed88ad640f3d76735f1e5dbc04b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4110cc2b5dc3aabd585a8e9a81855a12.png)
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解题方法
5 . 设曲线C的方程为x2+y2=2|x|-2|y|,则( )
A.曲线C既是轴对称图形,又是中心对称图形 |
B.曲线C围成图形的面积为![]() |
C.曲线C的周长为![]() |
D.曲线上任意两点间距离的最大值为4 |
您最近一年使用:0次
2023-11-23更新
|
313次组卷
|
3卷引用:江苏省曲塘高级中学2023-2024学年高二上学期期中考试数学试卷
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6 . 在平面直角坐标系
中,已知圆C的圆心在
上,且圆C与x轴相切,直线
,
.
(1)若直线
与圆C相切,求a的值;
(2)若直线
与圆C相交于A,B两点,将圆C分成的两段弧的弧长之比为
,且
,求圆C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfea30b3df4214f447aaeacbf558aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b138b5a47d97be0b954020002d9033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dd809d2f4f4f2287043eac970bf526.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5881f1ce9b4172ca346032d0fd1e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c48119b3932497634478f656c752ec4.png)
您最近一年使用:0次
2023-11-23更新
|
171次组卷
|
2卷引用:江苏省南京市2023-2024学年高二上学期期中调研测试数学试题
名校
7 . 已知圆
与圆
的公共弦所在直线与
轴垂直,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a622513ce7e19b9af5617606ba21a09c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b0211afae2d7e0d4f92351e1728f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2a39beea5adf5d07aea0424ca7a64f.png)
A.-4 | B.-2 | C.2 | D.4 |
您最近一年使用:0次
2023-11-23更新
|
248次组卷
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3卷引用:江苏省南京市2023-2024学年高二上学期期中调研测试数学试题
8 . 已知点
是椭圆
的上、下顶点,点
满足
.
(1)求点
的轨迹方程;
(2)经这点
的动直线
交椭圆
于
,
两点,若
与
的斜率之和为定值,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd6d152a6392eff03d96ebe61024b43.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)经这点
![](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/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/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
9 . 长方体
中,
,
,上底面
的中心为
,当点
在线段
上从
移动到
时,点
在平面
上的射影
的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4957406b21df59fdf7fa184752287b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b90bf8b51db7a4ff6e0678bd3d1ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
A.![]() | B.![]() | C.![]() | D. ![]() |
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10 . 椭圆
的弦
满足
,记坐标原点
在
的射影为
,则到直线
的距离为1的点
的个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09263551bca1d9256295c822a9faa75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2023-11-11更新
|
454次组卷
|
3卷引用:江苏省常州市第一中学2023-2024学年高二上学期11月期中数学试题