Find the equation of the surface that is the set of all poin

Find the equation of the surface that is the set of all points whose sum of their distances from the points (0,2,0) and (0,-2,0) equals 8.

It is an ellipsoid. with its axis along y-axis. center is at (0,0,0) => eqn of ellipsoid is (x^2/a^2)+ ( y^2/b^2)+ (z^2/c^2)= 1 measure a,b,c by checking that (a,0,0) and(0,b,0), (0,0,c) satisfy the distance constraint.