Finding equation of the circle passing through intersection of given circles and one other point

Question

Find the equation of the circle passing through the intersection of the circles $x^2+y^2-8x-2y+7=0$ and $x^2+y^2-4x+10y+8=0$ and through $(-1,-2)$.

To start out, how can I find their intersection points? It might help, but I can't do it.

Answer 1

$$x^2+y^2-8x-2y+7=0\text{ ...(1)}$$ $$x^2+y^2-4x+10y+8=0\text{ ...(2)}$$ $(1)-(2)$ we have, $-4x-12y-1=0$.
So $$y=\frac{4x+1}{-12}$$ Substitute $y=\frac{4x+1}{-12}$ into $(1)$ or $(2)$ to have a quadratic equation of $x$.