You are given a circle of radius 10 centered at the origin. Write down the equations of this circle

The equation of the circle has the form (x – a) ^ 2 + (y – b) ^ 2 = R ^ 2, where a and b are the coordinates of the center of this circle, R is its radius. The given circle has a center coinciding with the origin, so a = 0, b = 0. Substituting these values into the general equation of the circle, we get:
x ^ 2 + y ^ 2 = R ^ 2;
x ^ 2 + y ^ 2 = 10 ^ 2;
x ^ 2 + y ^ 2 = 100.