SOLUTION: center at the origin; a focus (0,2); vertex at (0,3)

The focus is closer to the center than the vertex ---> hence, the conic section is an ellipse.


A focus and a vertex lie on vertical line x= 0  ---> hence, the major axis is vertical.


The length of the major semi-axis is a = 3.


We find the length of the minor semi-axis b from the equation

    b = ,  where c is the eccentriciry  c= 2 (given).


So,  b =  =  = .


Thus the equation of the ellipse is


     +  = 1.