Find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.) Center at the origin, passing through P(5, −8)

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The equation of a circle fits the form (x - h)2 + (y - k)2 = r2 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 = r2 or just x2 + y2 = r2 but we still need to find the radius r (or at least r2 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. a2 + b2 = c2 or, in this case, (5)2 + (-8)2 = r2

So r2 = 25 + 64 = 89

We don't need to solve for "r" because the equation needs r2 and I now know that r2 = 89 so the equation x2 + y2 = r2 is now x2 + y2 = 89 and that's the answer!