We'll first clear a few points. 1. A hyperbola with horizontal axis and centred on origin (i.e. foci are centred on the x-axis) has equation x^2/a^2-y^2/b^2=1 (check: when y=0, x=+/- a, the vertices) The corresponding hyperbola with vertical axis centred on origin has equation y^2/a^2-x^2/b^2=1 (check: when x=0, y=+/- a, the vertices).
The co-vertex is the distance b in the above formula, such that the distance of the foci from the origin, c satisfies c^2=a^2+b^2. The rectangle with width a and height b has diagonals which are the asymptotes of the hyperbola.
We're given vertex = +/- 3, and covertex=+/- 5. And since vertices are situated at (3,0), and (-3,0), they are along the x-axis. So the equation must start with x^2/3^2.
It will be good practice for you to sketch all four hyperbolas given in the choices to fully understand the basics of a hyperbola.
