名校
解题方法
1 . 在平面直角坐标系中,已知动点M到点
与到直线
的距离相等.
(1)求动点M的轨迹E的方程;
(2)设点P是轨迹E上的动点,点Q,R在x轴上,圆
内切于
,求
的面积最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f772c3845894acb33c695f4e235fbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ede20ce638de73ac52d3c58122fd7dd.png)
(1)求动点M的轨迹E的方程;
(2)设点P是轨迹E上的动点,点Q,R在x轴上,圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ee1aeafdfc0aa7ae03e7336c81b1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
您最近一年使用:0次
2 . 在平面直角坐标系
中,一动圆经过点
且与直线
相切,设该动圆圆心的轨迹为曲线K, P是曲线K上一点.
(1)当
时,求曲线K的轨迹方程;
(2)已知过点A 且斜率为k的直线l与曲线K交于B,C 两点,若
且直线
与直线
交于Q点.求证:
为定值:
(3)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
且点 D,E在y轴上,
的内切圆的方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46110ded9a784e1e68684714746c9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853e3c15d116fb61f236ab239c50b114.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)已知过点A 且斜率为k的直线l与曲线K交于B,C 两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96968cc368104c626e7cdf658e361c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a249bee4ac9de17327ca5399e5077ca5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
您最近一年使用:0次
名校
解题方法
3 . 已知平面上一动点
到定点
的距离比到定直线
的距离小
,记动点
的轨迹为曲线
.
(1)求
的方程;
(2)点
为
上的两个动点,若
恰好为平行四边形
的其中三个顶点,且该平行四边形对角线的交点在第一、三象限的角平分线上,记平行四边形
的面积为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7b76d897de678faaf8221bafe217d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb93b19779fab3f7a6991633933a364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3687b9de2cd647ee49c4b9b01eac438a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45bd92770adca80f9aa3d2e4b7e106a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f790a1d74e757158ccac343e5dac6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab3e0100e6788858ab43861933dd248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab3e0100e6788858ab43861933dd248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4532e8175640973b48fa2bb4f53310.png)
您最近一年使用:0次
2024-03-08更新
|
1510次组卷
|
5卷引用:辽宁省八市八校2024届度高三第二次联合模拟考试数学试题
辽宁省八市八校2024届度高三第二次联合模拟考试数学试题2024届辽宁省名校联盟高考模拟卷(调研卷)数学试题(一)(已下线)专题8.4 抛物线综合【八大题型】(已下线)重难点14 圆锥曲线必考压轴解答题全归类【十一大题型】(举一反三)(新高考专用)-1(已下线)专题1 几何条件代数化【练】(压轴题大全)
4 . 已知点
在抛物线
上运动,过点
的两直线
与圆
相切,切点分别为
,当
取最小值时,直线
的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617d3975f2f3a55ebe30ec8001db6052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0873a0f3245544b4451ec5d2570dbe41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228bf1b66b2651cb40ec6912fc84b115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-02-29更新
|
584次组卷
|
3卷引用:辽宁省沈阳市第一二〇中学2023-2024学年高三第十次质量监测(最后一卷)数学试题
解题方法
5 . 已知正方体
的棱长为
分别是棱
和
的中点,
是棱
上的一点,
是正方形
内一动点,且点
到直线
与直线
的距离相等,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd110e5d9ab042968ec706b44e78572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() |
B.点![]() ![]() ![]() |
C.存在点![]() ![]() ![]() ![]() |
D.动点![]() |
您最近一年使用:0次
2024-02-24更新
|
215次组卷
|
4卷引用:河南省濮阳市2023-2024学年高二上学期期末考试数学试题
6 . 抛物线
被直线
截得的弦的中点
的纵坐标为1.
(1)求
的值及抛物线的准线方程;
(2)过抛物线的焦点
作两条互相垂直的直线
,
,直线
与拋物线相交于
,
两点,直线
与抛物线相交于
,
两点,求四边形
的面积
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d6e08526a91f8dfd160e7da2f92a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过抛物线的焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/3f6f17bc385bafb37e8f964e5eb99cd0.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/9c593ebdb2f1934a0cb56f8c44f454f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
7 . 已知抛物线
,过焦点
的直线交抛物线于
两点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6116a847c87704efd0b439f866072a7.png)
(1)求抛物线
的方程;
(2)若抛物线上有一动弦
为弦
的中点,
,求点
的纵坐标的最小值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6116a847c87704efd0b439f866072a7.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若抛物线上有一动弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3488e7db6905173e8a6b306afe1c073d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5c259fd573be2a9457298a4f26394d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
8 . 已知抛物线
过点
.
(1)求抛物线C的焦点到准线的距离.
(2)已知点
,过点
的直线l交抛物线C于点M、N,直线
分别交直线
于点P、Q,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941a1c49b132e8295d3cb92542befce5.png)
(1)求抛物线C的焦点到准线的距离.
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee07d86765c4fb74ac647742f16bd57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d075e1f6049129308db0cc58e3916e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d9d3102e916e7f1900b39f4b8b2868.png)
您最近一年使用:0次
名校
解题方法
9 . 已知抛物线
上的三点
,B,C,直线AB,AC是圆
的两条切线,则直线BC的方程为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec68c680d1b8c8cfa98b48a27d2c46a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81550d38bd047ac4c6c0ffadc3712491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277e8382533e3ba18e213ea19ce6b9cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/96ae584d-41ad-4033-8665-1db4b86155fd.png?resizew=166)
您最近一年使用:0次
2024-01-30更新
|
302次组卷
|
2卷引用:江苏省镇江第一中学2022-2023学年高二上学期期末考试数学试题
名校
解题方法
10 . 在平面直角坐标系
中,抛物线
的焦点为
,
,
,
为抛物线
上的任意三点(异于
点),
,则下列说法不正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6050b7ee89e71e1bda14bed616995296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8399d619607137a72f985ebb1276131.png)
A.![]() |
B.若![]() ![]() |
C.设![]() ![]() ![]() ![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次