Find the equation of circle passing through (1,1) and the point of intersection of the circles $x^2+y^2+10x-y=0$ and $2x^2+2y^2+2x-5y-23=0$

Question

$\begin{array}{1 1}(a)\;(x^2-y^2-10x-y)+\large\frac{22}{23}\normalsize(x^2+y^2+x-3y-\large\frac{23}{2})\normalsize=0\\(b)\;(x^2+y^2+10x-y)+\large\frac{22}{23}\normalsize(x^2+y^2+x-3y-\large\frac{23}{2})\normalsize=0\\(c)\;(x^2-y^2-10x-y)+\large\frac{23}{22}\normalsize(x^2+y^2+x-3y-\large\frac{23}{2})\normalsize=0\\(d)\;(x^2-y^2-10x-y)+\large\frac{12}{23}\normalsize(x^2+y^2+x-3y-\large\frac{23}{2})\normalsize=0\end{array}$