The equation of a circle with center at (h,k) and radius r is:
Since you are centered at the origin, h and k are both zero, so:
Just pick x = 10, x = -10, and x = 0 and substitute these values then solve for y. That will give you 4 of the 6 points you need. Then pick another value for x other than zero on the interval -10 < x < 10 to get your last two points.