Question

# Find the equation of the hyperbola whose vertices are (0, ±3) and the foci are (0, ±5).

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Solution

## 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). ∴ a=3. Let its foci be (0, ±c). But, it is given that the foci are (0, ±5). ∴ c=5. Now, b2=(c2−a2)=(52−32)=(25−9)=16. Thus, a2=32=9 and b2=16. Hence, the required equation is y29−x216=1.

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