Geo4.97

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Find the equation of the circle which touches the line x=y\, at the origin and passes through the point (2,1)\,.

Equation to the point circle of the origin is

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

Given tangent line x-y=0\,

The circle touching teh line and at origin is x^{2}+y^{2}+k(x-y)=0\,

This circle passes through the point(2,1)

Hence

4+1+k(2-1)=0\,

k=-5\,

Equation to the required circle is

x^{2}+y^{2}-5x+5y=0\,

Main Page:Geometry:Circles