find the equation of an elipse whose vertices are (2, -2) and (2, 4) and whose eccentricity is 1/3

Answer 1

clearly the ellipse has a vertical major axis
centre is (2,1) , b = 3

For this ellipse: e = c/b
1/3 = c/3
c = 1

a^2 + c^2 = b^2
a^1 + 1 = 9
a^2 = 8

(x-2)^2/8 + (y-1)^2/9 = 1