过两圆x²+y²-1=0和x²+y²-4x=0的交点且与直线x-√3y-6=0相切的圆的方程
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![过两圆x²+y²-1=0和x²+y²-4x=0的交点且与直线x-√3y-6=0相切的圆的方程](/uploads/image/z/2493496-64-6.jpg?t=%E8%BF%87%E4%B8%A4%E5%9C%86x%26%23178%3B%2By%26%23178%3B-1%3D0%E5%92%8Cx%26%23178%3B%2By%26%23178%3B-4x%3D0%E7%9A%84%E4%BA%A4%E7%82%B9%E4%B8%94%E4%B8%8E%E7%9B%B4%E7%BA%BFx-%E2%88%9A3y-6%3D0%E7%9B%B8%E5%88%87%E7%9A%84%E5%9C%86%E7%9A%84%E6%96%B9%E7%A8%8B)
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过两圆x²+y²-1=0和x²+y²-4x=0的交点且与直线x-√3y-6=0相切的圆的方程
过两圆x²+y²-1=0和x²+y²-4x=0的交点且与直线x-√3y-6=0相切的圆的方程
过两圆x²+y²-1=0和x²+y²-4x=0的交点且与直线x-√3y-6=0相切的圆的方程
x^2+y^2-1=0......(1)
x^2+y^2-4x=0......(2)
(1)-(2):
x=1/4,y=±√15/4
C(a,0)
x-√3y-6=0
r=d=|a-√3*0-6|/2=|a-6|/2
r^2=(a-1/4)^2+(√15/4)^2=(|a-6|/2)^2
a=2,-16/3
r=2,17/3
C1:(x-2)^2+y^2=4
C2:(x+16/3)^2+y^2=289/9
C1是原来的圆,答案是C2