The only difference (aside from the values of the coefficients) between the equation of the hyperbola that I just showed you earlier and an ellipse is that a hyperbola has a minus sign between the two fractions on the left and an ellipse has a plus sign. The process of completing the squares is the same.
An ellipse centered at (h,k) with a semi-major axis a, and a semi-minor axis b is given by:
Notice that if a = b and then you multiply by the now common denominator, you get the equation of a circle centered at (h,k) with radius a.
