find the standard form of the equationof the ellipse satisfying the following conditions

Question

center at (2,3); minor axis vertical, with length 8; c=3

Answer 1

(x-2)^2/a^2+(y-3)^2/b^2=1 where a = semi-major axis length, b = semi-minor axis length = 8/2 = 4.

Focus c=√(a^2-b^2) where b=length of semi-minor axis=4; 3=√(a^2-b^2), 9=a^2-16, a^2=25, a=5.

Equation of ellipse in SF is (x-2)^2/25+(y-3)^/16=1.