题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211301-50260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211301-66135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-11682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-39358.gif)
(1)求点H(x,y)的轨迹G的方程;
(2)已知P(-1,0)、Q(1,0),M是曲线G上的一点,那么
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-77293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-93251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-42843.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211304-94846.gif)
解析
由定比分点坐标公式可知,A点的坐标为(x,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211304-95808.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211304-46355.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211304-56504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211304-95808.gif)
由BH⊥CA知x2-4+
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211304-95808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-93251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-42843.gif)
∴G的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-93251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-42843.gif)
(2)解法一:显然P、Q恰好为G的两个焦点,
∴|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-75115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-43728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-83859.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-77293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-10026.gif)
∴|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-75115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-43728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-75115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-43728.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-74183.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-75115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-43728.gif)
∴M点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-93251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-42843.gif)
∴当M点的坐标为(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-57359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-57359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-77293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
解法二:设M点的坐标为(x,y),
显然P、Q恰好为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-93251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-42843.gif)
∴|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-75115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-43728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-83859.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-77293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-10026.gif)
由椭圆第二定义可得|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-75115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211305-43728.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-36703.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211307-90142.gif)
∴M点的坐标为(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-57359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-57359.gif)
∴当M点的坐标为(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-57359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211306-57359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211302-20226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-77293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211303-15859.gif)
核心考点
试题【在△ABC中,已知B(-2,0)、C(2,0),AD⊥BC于点D,△ABC的垂心为H,且=.(1)求点H(x,y)的轨迹G的方程;(2)已知P(-1,0)、Q(】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211255-38854.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211255-42555.gif)
A.b2 | B.ab |
C.ac | D.bc |
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211241-37714.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211237-50500.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023211232-35167.gif)
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