Geo4.114

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Find the radical centre of the circles x^{2}+y^{2}-4x-2y+6=0,x^{2}+y^{2}-2x+6y=0,x^{2}+y^{2}-12x+2y+30=0\,

Let the equations be S_{1},S_{2},S_{3}\,

Radical axis of S1 and S2 is

S_{1}-S_{2}=0\,

2x+8y-6=0,x+4y-3=0\,

The radical axis of the S2 and S3 is

10x+4y-30=0,5x+2y-15=0\,

Solving these two equations

y=0,x=3\,

Therefore,the radical centre is (3,0).


Main Page:Geometry:Circles