Which of the following equations correctly represents a circle centered at the origin with a radius of 10?

We need only focus on the standard equation of a circle centered at the origin with radius r: x^2 + y^2 = r^2. Here, r = 10 and so r^2 = 100.

Thus, in this case, the equation of the circle is x^2 + y^2 = 10^2.