In each of the following find the equations of the hyperbola satisfying the given conditions

Question

In each of the following find the equations of the hyperbola satisfying the given conditions vertices (0, ± 6),

Philoid · Accepted Answer

Given: Vertices (0, ±6),

To find: equation of the hyperbola

Formula used:

The standard form of the equation of the hyperbola is,

Coordinates of the vertices for a standard hyperbola is given by (0, ±b)

According to question:

b = 6 ⇒ b² = 36

We know,

a² = b²(e² – 1)

⇒ a² = 64

Hence, equation of hyperbola is: