Geo4.24

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Find the equation of the circle which passes through the points of intersection of x^{2}+y^{2}-x-y=0\, and x+y=1\, and also through the point (1,1).

The formula for equation to the circle is

S+\lambda L=0\, where S=equation of the given circle and L=equation of the line and Lambda is a constant

Hence the equation of the circle is

(x^{2}+y^{2}-x-y)+\lambda (x+y-1)=0\,

This circle passes through the point (1,1)

Now

(1^{2}+1^{2}-1-1)+\lambda (1+1-1)=0\,

\lambda =0\,

Hence the equation of the circle is

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


Main Page:Geometry:Circles