Since the center is at the origin, the vertices will have to be on the x- and/or y-axes. (I say "and/or" depending on how the book defined "vertices"; they may just be the endpoints of the major axis, not the minor).
The center-axis formula for an ellipse is, I believe, something along the lines of the following:
. . . . .\(\displaystyle \Large{\frac{(x\mbox{ }-\mbox{ }h)^2}{a^2}\mbox{ }+\mbox{ }\frac{(y\mbox{ }-\mbox{ }k)^2}{b^2}\mbox{ }=\mbox{ }1}\)
...where the center is at (x, y) = (h, k). The book should give some relationship (very nice and neat) between the values "a" and "b" and the lengths of the major and minor axes. From this information, the vertices should be easily determined.
Eliz.