The equation for an ellipse with its center at the origin (0,0), foci at (0, ±c), and covertices at (±a, 0) is:
(x^2 / a^2) + (y^2 / b^2) = 1
In this case, the distance from the origin to each focus is c = 3, and the distance from the origin to each covertex is a = 2.
So, plugging in these values, the equation becomes:
(x^2 / 2^2) + (y^2 / 3^2) = 1
Simplifying:
(x^2 / 4) + (y^2 / 9) = 1
This is the equation of the ellipse with the given properties.