Ellipse equation.? Doubts?

Let "b" represent half the length of the minor axis. Then
.. b = 4/2 = 2
Let "c" represent the distance from the center to the focus. It is given as
.. c = √5
Now the length "a" of half the major axis can be found as
.. a^2 = b^2 + c^2
.. a^2 = 2^2 + (√5)^2
.. a^2 = 4 + 5 = 9
.. a = √9 = 3

The given focus is on the y-axis below the center of the ellipse, so the long axis is in the y-direction. The equation can be written as
.. (x-0)^2/b^2 + (y-0)^2/a^2 = 1 ... where (0, 0) is the center of the ellipse
.. x^2/4 + y^2/9 = 1