In each of the following find the equations of the hyperbola satisfying the given conditions
vertices (0, ± 5), foci (0, ± 8)
Given: Vertices are (0, ±5) and foci are (0, ±8)
To find: equation of the hyperbola
Formula used:
The standard form of the equation of the hyperbola is,
Vertices of the hyperbola are given by (0, ±b)
Foci of the hyperbola are given by (0, ±be)
Vertices are (0, ±5) and foci are (0, ±8)
Therefore,
a2 = b2(e2 – 1)
⇒ a2 = 39
The equation of hyperbola:
Hence, the required equation of the hyperbola is