The distance between the foci of a hyperbola is 16 and its eccentricity is , then equation of the hyperbola is

Question

Philoid · Accepted Answer

Given: Distance between foci is 16 and eccentricity is

To find: equation of the hyperbola

Formula used:

Standard form of the equation of hyperbola is,

Distance between foci is given by 2ae

According to question:

2ae = 16

⇒ a² = 32

We know,

b² = a²(e² – 1)

⇒ b² = 32

Hence, equation of hyperbola is:

⇒ x² – y² = 32