Geo4.104

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Find the equation passing through the origin and which has its centre on the linex+y=4\, and cuts circle x^{2}+y^{2}-4x+2y+4=0\, orthogonally.

Let the the required circle be

x^{2}+y^{2}+2gx+2fy+c=0\,

This circle passes through the origin,hence c=0.

The centre lies on the given line,hence

-g-f=4\,

g+f=-4\,

From the given circle

g_{1}=-2,f_{1}=1,c=4\,

2(-2)(g)+2(1)(f)=4\,

-2g+f=2\,

Solving these two equations we get

g=-2,f=-2\,

Therefore,the required circle equation is

x^{2}+y^{2}-4x-4y=0\,


Main Page:Geometry:Circles