Find the coordinates of the points where the two circles intersect.

Question

The two circles are:

$1$) $$(x-2)^2 + (y+1)^2 = 25$$

$2$) $$(y-2)^2 + (x+1)^2 = 25$$

Answer 1

$(1)$ and $(2)$ are symmetric for $x=y$. The two points you are looking for are the intersenction between $(1)$ and $y=x$.

Therefore, the intersections are $(\frac{1 \pm \sqrt{41}}{2},\frac{1 \pm \sqrt{41}}{2})$.