Question

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^{2}}{25}$+ $\frac{y^{2}}{9}$= 1. The equation of the hyperbola if its eccentricity is 2, is-

• A. $\frac{x^{2}}{4}$– $\frac{y^{2}}{12}$= 1
• B. $\frac{x^{2}}{12}$–$\frac{y^{2}}{4}$= 1
• C. $\frac{x^{2}}{12}$–$\frac{y^{2}}{16}$= 1
• D. None of these

Answer 1

Answer: (A)

$\frac{x^{2}}{4}$– $\frac{y^{2}}{12}$= 1

Answer 2

Foci of ellipse (±4, 0) Ž Foci of hyperbola(± 4, 0)

ae = 4 Ž e = 2 Ž a = 2

Ž b² = a²(e² – 1) = 4(4 – 1) = 12