The foci of the ellipse are equidistant from its origin at (-25,0) and (25,0), so the origin must be at x=0 (y axis). The length of the semi major axis is 25.
The covertices at (0,-15) and (0,15) are equidistant from the origin, fixing the origin at (0,0). The length of the semi minor axis is 15.
The equation of the ellipse in standard form is:
x²/25²+y²/15²=1 which can also be written:
x²/625+y²/225=1.