**The equation of a circle fits the form (x - h) ^{2} + (y - k)^{2} = r^{2} where the center is at the point (h, k) and the radius is "r".**

**In this case, since the center is at the origin (0, 0), then it simplifies to (x - 0) ^{2} + (y - 0)^{2} = r^{2} or just x^{2} + y^{2} = r^{2} but we still need to find the radius r (or at least r^{2} because that is what will go in the equation). To find the radius, it might be useful to look at the graph:**

**I showed the point (5, -8) on the circle and then I showed the radius and labeled it "r". Notice that I can make a triangle with one side 5 (because that is the x-coordinate of the point) and one side -8 (because that is the y-coordinate of the point). Then I can use the Pythagorean Theorem. a ^{2} + b^{2} = c^{2} or, in this case, (5)^{2} + (-8)^{2} = r^{2}**

**So r ^{2} = 25 + 64 = 89**

**We don't need to solve for "r" because the equation needs r ^{2} and I now know that r^{2} = 89 so the equation x^{2} + y^{2} = r^{2} is now x^{2} + y^{2} = 89 and that's the answer!**