名校
解题方法
1 . 已知圆
,点
是圆
上的动点,过点
作
轴的垂线,垂足为
.
(1)已知直线
:
与圆
相切,求直线
的方程;
(2)若点
满足
,求点
的轨迹方程;
(3)若过点
且斜率分别为
的两条直线与(2)中
的轨迹分别交于点
、
,
、
,并满足
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01268ac8e838d0f45ccb35bc1d479d0.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77462bdf303d687ce5241a413cc9db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01268ac8e838d0f45ccb35bc1d479d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d2c8415d70008be53ae18111b96e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb15d572f57b05bdb7171622323b900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a244e94d026b6bf92d9779a95387b5d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2022-03-27更新
|
814次组卷
|
2卷引用:江苏省常州市第一中学2021-2022学年高二上学期12月学习质量检测数学试题
名校
解题方法
2 . 设
、
分别是椭圆
的左、右焦点,过
直线l与椭圆E相交于A,B两点.
(1)当t为常数时.若
成等差数列,且公差不为0,求直线l的方程:
(2)当
时,延长
与E相交于另一个点C,试判断直线
与椭圆
位置关系,并说明理由.
![](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/9480823672eaa32df41fbe0a878c36cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)当t为常数时.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2456e705edaefb8e04abf14ddd0f4a3f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245985a19e6b0744248b026c29ba4b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a80a5faf097bfc8bafbef34138be0b.png)
您最近一年使用:0次
2021高二·江苏·专题练习
名校
3 . 抛物线C:
的焦点为F,P为其上一动点,当P运动到
时,
,直线l与抛物线相交于A,B两点,点
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32293d25fb98c1d6b858234b23081010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a0328dde917c3e6d0f1ca9ddb6027b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2a5c155717f3a59d7818b4bbdf44e9.png)
A.抛物线的方程为![]() |
B.![]() |
C.当直线l过焦点F时,以AF为直径的圆与x轴相切 |
D.若过A,B的抛物线的两条切线交准线于点T,则A,B两点的纵坐标之和最小值为2 |
您最近一年使用:0次
21-22高二·江苏·单元测试
解题方法
4 . 已知圆
,点
,点Q在圆
上运动,
的垂直平分线交
于点P.
(1)求动点P的轨迹的方程C;
(2)设
分别是曲线C上的两个不同点,且点M在第一象限,点N在第三象限,若
,O为坐标原点,求直线MN的斜率;
(3)过点
的动直线l交曲线C于
两点,在y轴上是否存在定点T,使以AB为直径的圆恒过这个点?若存在,求出点T的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4463d26d5bb4a96f11cffdfa2aad480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16c755ab3fea6ca99b13193a5d7e485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30a7506331e47342fb1e7d2e12d041.png)
(1)求动点P的轨迹的方程C;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12967e4f8c1e2e29c1999caa62f79b71.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6831c6674f4bf86df7c8dd730e1c187d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
您最近一年使用:0次
21-22高二·江苏·单元测试
名校
解题方法
5 . 已知椭圆C:
的左、右顶点分别为A,B,F为椭圆C的右焦点,圆
上有一动点P,P不同于A,B两点,直线PA与椭圆C交于点Q,
,
分别为直线BP,QF的斜率,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02aece2d026376eed9c9b3ee67a4cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4c3d1d76ee04f281aaef5f99a41a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f980ccb6f902d460d0ea2920bfe2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036c2308c7a211f0f044c49f04655419.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-01-03更新
|
1663次组卷
|
3卷引用:专题18 《圆锥曲线与方程》中的动点动直线问题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
(已下线)专题18 《圆锥曲线与方程》中的动点动直线问题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) 重庆市天星桥中学2022届高三上学期学业质量调研抽测(一)数学试题四川省遂宁中学校2021-2022学年高二下学期期中考试数学(理)试题
21-22高二·江苏·单元测试
名校
解题方法
6 . 如图,过抛物线
的焦点F作两条互相垂直的弦AB、CD,若
与
面积之和的最小值为32,则抛物线的方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e64c953aaf341e772a5fe776fbc78a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e5fe0afb-d043-4931-819b-424e03a4fcb0.png?resizew=176)
您最近一年使用:0次
7 . 1.在平面直角坐标系xOy中,已知点
,点M满足
.记M的轨迹为C.
(1)求C的方程;
(2)点T在直线x=4上,过T的两条直线分别交C于A,B两点和P,Q两点,且|TA|·|TB|=|TP|·|TQ|,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10f5be271d5e18347e2792d348e5411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b549d39d7e273f5ba461f1d508b20dc.png)
(1)求C的方程;
(2)点T在直线x=4上,过T的两条直线分别交C于A,B两点和P,Q两点,且|TA|·|TB|=|TP|·|TQ|,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18cad6ab2dd26fb28da19be0f8358265.png)
您最近一年使用:0次
解题方法
8 . 如图,抛物线
(
)的焦点为椭圆
的的右焦点,
为椭圆的右顶点,
为坐标原点.过
的直线
交抛物线
于
,
两点,射线
,
分别交椭圆
于
,
两点.
![](https://img.xkw.com/dksih/QBM/2021/11/17/2853474462130176/2865272768954368/STEM/c0628963ffce47f0be0389595bb76431.png?resizew=239)
(1)求抛物线
的方程,并证明
点在以
为直径的圆的内部;
(2)记
,
的面积分别为
,
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c156c3b344e637b4f86404f2711940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d323869f1ee79f8d629fe70d72c538fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2021/11/17/2853474462130176/2865272768954368/STEM/c0628963ffce47f0be0389595bb76431.png?resizew=239)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc869125145c0139d92490a41bd3918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1062304efa02843fcd70a8864989cdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
9 . 已知圆
,点
是圆
上的动点,过点
作
轴的垂线,垂足为
.
(1)若点
满足
,求点
的轨迹方程;
(2)若过点
且斜率分别为
的两条直线与(1)中
的轨迹分别交于点
、
,
、
,并满足
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01268ac8e838d0f45ccb35bc1d479d0.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fa696f42eb38eb8e18b5bc5eca4c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb15d572f57b05bdb7171622323b900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5538d4c428da90edee6ca488a244dfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
名校
解题方法
10 . O为坐标原点椭圆
的左右焦点分别为
,离心率为
;双曲线
的左右焦点分别为
,离心率为
,已知
,切
.
(1)求
的方程;
(2)过
作
的不垂直于y轴的弦
,M为
的中点,当直线
与
交于P,Q两点时,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e376b48dacaa422f4d21afe48c32523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626706e779756baf8f7aa4cd276d2017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d5d4af8df621f4011f7a8d7dcf6257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0859620b0628987cfdb941c2e4c788.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
您最近一年使用:0次
2021-11-22更新
|
1581次组卷
|
5卷引用:江苏省徐州市第一中学2021-2022学年高二上学期期中数学试题
江苏省徐州市第一中学2021-2022学年高二上学期期中数学试题(已下线)3.2.2 双曲线的几何性质(难点)-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)考点42 圆锥曲线中的范围与最值问题-备战2022年高考数学典型试题解读与变式(已下线)专题30 圆锥曲线三角形面积与四边形面积题型全归类-2(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)