Find the equation of the hyperbola whose vertices are (0, ±3) and the foci are (0, ±5).
Since the vertices of the given hyperbola are of the form (0, ±a), it is a vertical hyperbola.
Let the required equation be y2a2−x2b2=1.
Then, its vertices are (0, ±a).
But, it is given that the vertices are (0, ±3).
Let its foci be (0, ±c).
But, it is given that the foci are (0, ±5).
Thus, a2=32=9 and b2=16.
Hence, the required equation is y29−x216=1.