Practice!

Sample Problem

Find the standard form of the equation of a hyperbola (centered at the origin) with vertices (0, ±2) and foci (0, ±5).

Solution

Since the vertices (0, ±2) are 2 units away from the center (0,0), a=2. Since the foci (0, ±5) are 5 units away from the center (0,0), c=5.

From c2=a2+b2, we can find b:

b2=c2-a2=52-22=21

b=√21

Since the vertices and foci all share the same x-coordinate, we know this hyperbola has a transverse axis that is vertical. Therefore, our equation for this hyperbola is