Geo4.115

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Find the radical centre of the circles x^{2}+y^{2}-2x=0,x^{2}+y^{2}+2x=0,x^{2}+y^{2}-2y=0\,

Let the equations S1,S2,S3.

The radical axis of the first two circles is

(x^{2}+y^{2}-2x)-(x^{2}+y^{2}+2x)=0\,

x=0\,

Radical axis of the second and third equations is

(x^{2}+y^{2}+2x)-(x^{2}+y^{2}-2y)=0\,

2x+2y=0,x+y=0,x=-y\,

Therefore the radical centre is (0,0)


Main Page:Geometry:Circles