Find the equation of the cricle passing through (1,1) and the points of intersection of the circels `x^(2)+y^(2)+13x-3y=0and2x^(2)+2y^(2)+4x-7y-25=0`.

Explanation

Equation of the circle passing through the points of intersection of the given circles is
`(x^(2)+y^(2)+13x-3y)+lambda(2x^(2)+2y^(2)+4x-7y-25)=0` (1)
If this circle passes through the point (1,1), then
`(1+1+13-3)+lambda(2+2+4-7-25)=0`
`implies lambda = 1//2`
Substituting `lambda =1//2` in (1), we get the equation of the required circle as `4x^(2)+4y^(2)+30x-13y-25=0`.