It is known that the center of the ellipse is at the origin, the focus is on the y-axis, the focal length is 4, and the eccentricity is 2 / 3

It is known that the center of the ellipse is at the origin, the focus is on the y-axis, the focal length is 4, and the eccentricity is 2 / 3

The focal length is 4, C = 4 / 2 = 2
The centrifugal ratio is 2 / 3, e = C / a = 2 / a = 2 / 3
a=3
c^2=a^2-b^2
4=9-b^2
b^2=5
The center of the ellipse is at the origin and the focus is on the Y axis
Elliptic equation: y ^ 2 / 9 + x ^ 2 / 5 = 1