过点A（5,0）且与圆B(x+5)^2+y^2=36相切的圆的圆心轨迹方程

过点A（5,0）且与圆B(x+5)^2+y^2=36相切的圆的圆心轨迹方程
过点A（5,0）且与圆B(x+5)^2+y^2=36相切的圆的圆心轨迹方程

过点A（5,0）且与圆B(x+5)^2+y^2=36相切的圆的圆心轨迹方程
圆心C(x,y)
R=√[(x-5)²+y²]
圆心B(-5,0),r=5
圆心距d=√[(x+5)²+y²]
相切
d=R+r或|R-r|
d=R+r
√[(x+5)²+y²]=√[(x-5)²+y²]+5
√[(x+5)²+y²]-√[(x-5)²+y²]=5
到(-5,0)距离减去到(5,0)距离是定值5
是双曲线的一支
2a=5,a=5/2
c=5
b²=25-25/4=75/4
x²/(25/4)-y²/(75/4)=1
离(-5,0)更远,
是右支
x²/(25/4)-y²/(75/4)=1,x>0
d=|R-r|
√[(x+5)²+y²]=|√[(x-5)²+y²]-5|
x²+10x+25+y²=x²-10x+25+y²-10√[(x-5)²+y²]+25
4x-5=-2√[(x-5)²+y²]
所以4x-5<=0,x<=5/4
16x²-40x+25=4x²-40x+100+4y²
12x²-4y²=75
x²/(25/4)-y²/(75/4)=1
x<=5/4,就是x<0
所以
x²/(25/4)-y²/(75/4)=1