The coordinates of a point P$(x,y)$ satisfy $x^2+y^2=169$. What does that tell you about P?

The distance of P$(x,y)$ from the origin is $\sqrt{x^2+y^2}$. Here that equals $\sqrt{169}=13$ for every point satisfying the condition, so each such P is 13 units from O and the whole set forms a circle of radius 13 about the origin. Reading off 169 forgets the square root; (0, 13) and (13, 0) are only two members of the set, since (5, 12) and (-12, 5) also satisfy it.