Question

If hyperbola $\frac{x^{2}}{b^{2}} - \frac{y^{2}}{a^{2}}$ = 1 passes through the focus of ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 then eccentricity of hyperbola is-

• A. $\sqrt{2}$
• B. $\frac{2}{\sqrt{3}}$
• C. $\sqrt{3}$
• D. None of these

Answer 1

Answer: (C)

$\sqrt{3}$

Answer 2

Let e₁ & e₂ are the eccentricity of ellipse & hyperbola

Q b = ae₁ …(1)

b² = a² (1 – $e_{1}^{2}$) …(2)

a² = b² ($e_{2}^{2}$ – 1) …(3)

From (1) & (2) 2$e_{1}^{2}$ = 1 Ю e₁ = 1/$\sqrt{2}$

From (1) & (3) 2 = $e_{2}^{2}$ – 1 Ю e₂ = $\sqrt{3}$