Question

The foci of a hyperbola coincide with the foci of the ellipse `x^2/25 + y^2/9` = 1. Find the equation of the hyperbola, if its eccentricity is 2.

विकल्प

• `x^2/4 - y^2/12` = 1

• `x^2/4 - y^2/12` = 2

• `x^2/9 - y^2/45` = 1

• `x^2/2 - y^2/10` = 1

Answer 1

`bb(x^2/4 - y^2/12 = 1)`

Explanation:

Foci of ellipse (–4, 0)(4, 0)

9 = 25 (1 – e²)

e = `4/5`

Focus (4, 0) of hyperbola

e = 2

b² = a²(e² – 1)

ae = 4

a = 2

⇒ a² = 4

b² = 12

Equation of hyperbola `x^2/4 - y^2/12` = 1