已知椭圆
:
的左顶点为
,过原点
的直线(与坐标轴不重合)与椭圆
交于
两点,直线
、
分别与
轴交于
两点.问:以
为直径的圆是否经过定点?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
2024高三下·全国·专题练习 查看更多[3]
(已下线)第22题 代数几何比翼齐飞,动静互变化难为易(优质好题一题多解)(已下线)第30题 几何分析曲径通幽,代数推演水到渠成(优质好题一题多解)(已下线)模块7专题6 正交于顶 模型优先练
更新时间:2024-05-09 15:37:58
|
相似题推荐
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐1】已知圆
,直线
.
(1)若点P在直线l上运动,过点P作圆O的两条切线
,切点分别为
,求证:过点
的圆过定点,并求出所有定点的坐标;
(2)若点P在直线l上运动,过点P作圆O的两条切线
,切点分别为
,求证:直线AB过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bba341d6dc102851c557072f738ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82503069ae1dda33bb96fdddbe1c87c6.png)
(1)若点P在直线l上运动,过点P作圆O的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e7f54c3c611633cf0e2fe218d89460.png)
(2)若点P在直线l上运动,过点P作圆O的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
您最近一年使用:0次
【推荐2】在平面直角坐标系
中,①已知点
,直线
,动点P满足到点Q的距离与到直线
的距离之比为
.②已知点
是圆
上一个动点,线段HG的垂直平分线交GE于P.③点
分别在
轴,y轴上运动,且
,动点P满足
.
(1)在①,②,③这三个条件中任选一个,求动点P的轨迹C的方程;
(注:如果选择多个条件分别解答,按第一个解答计分)
(2)设圆
上任意一点A处的切线交轨迹C于M,N两点,试判断以MN为直径的圆是否过定点?若过定点,求出该定点坐标.若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972cef3d3c6ff94cdc58ecaf9e2d7d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b4bd11e0cee8930366898110d222cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68af022d7b0bbdd0597e7ce6251f7413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d42c33a7a73cf62db85124edb35e496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a99e8a76fddaef080a96857d6df2a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1354e337e9aef6a90ae478303282fc1.png)
(1)在①,②,③这三个条件中任选一个,求动点P的轨迹C的方程;
(注:如果选择多个条件分别解答,按第一个解答计分)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
解题方法
【推荐1】已知椭圆
:
(
)的离心率为
,
为椭圆
上位于第一象限内的一点.
(1)若点
的坐标为
,求椭圆
的标准方程;
(2)设
为椭圆
的左顶点,
为椭圆
上一点,且
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e344a492fabcbfa4f6514df49bdc880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf86e99d40dc6702c02cb481c55b7e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
解答题
|
适中
(0.65)
【推荐2】设椭圆
,直线
与椭圆交于
两点,当
经过椭圆的一个焦点和一个顶点时,
.
(Ⅰ)求椭圆的方程;
(Ⅱ)若直线
的斜率成等差数列(
是坐标原点),求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327a8132cb929667c033a3c20bd9c67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98a71c08afcc84d7607183121adee7e.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fd2722d23f6fb6d32b54865bd6af70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8189f7b0ffe4d20bf0fad43b4ed589.png)
您最近一年使用:0次