This circle is centered at the origin, and the length of its radius is 10. what is the circle's equation?

The equation of the circle that you are looking for is x^2 + y^2 = 100.

You can find this by using the base formula for a circle:

(x - x1) ^2 + (y - y1) ^2 = r^2

In which x1 is the x-coordinate of the origin, y1 is the y-coordinate of the origin, and r is the radius. So we put in the values we know and simplify.

(x - 0) ^2 + (y - 0) ^2 = 10^2

x^2 + y^2 = 100