# Find the coordinates of the points where the two circles intersect. [duplicate]

The two circles are:

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

## marked as duplicate by user228113, Claude Leibovici, Frunobulax, Harish Chandra Rajpoot, Pierre-Guy PlamondonFeb 22 '16 at 12:40

• Set $(1) = (2)$. You will get a relation between $x$ and $y$. Substitute in any equation to get the point(s) of intersection. – SS_C4 Feb 22 '16 at 8:01
$(1)$ 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 $(\frac{1 \pm \sqrt{41}}{2},\frac{1 \pm \sqrt{41}}{2})$.