What information do you need to write the equation of a circle with a center at the origin?

Just its radius

Step-by-step explanation:

The equation of the circle is the following:

(x-a) ^2 + (y-b) ^2 = r^2 where (a, b) is the center and r the radius

If you want to do it in the origin, would be,

x^2 + y^2 = r^2