What is the standard equation for the circle passing through (0,9) centered at the origin

Start with x^2 + y^2 = r^2, where r signifies radius. Subst. 0 for x and 9 for y:

0^2 + 9^2 = r^2. Therefore, r = 9.

The std eqn is x^2 + y^2 = 9^2. this is a special case of

(x-h) ^2 + (y-k) ^2 = r^2 and is appropriate because the origin is at (0,0).