Write an equation for the circle that satisfies each set of conditions?

Center at 7,-3  and passes thru the origin...

  Radius is distance from center to origin

     sqrt(7^2 +3^2) = SQRT 58 = r

 

circle with center at h,k      (x-h)^2 +(y-k)^2 = r^2

so the circle in question is given by        (x-7)^2 + (y+3)^2 = 58