Question

The eccentricity of an ellipse whose pair of a conjugate diameter are y = x and 3y = -2x is

• A. 2/3
• B. 1/3
• C. 1/$\sqrt{3}$
• D. None of these

Answer 1

Answer: (C)

1/$\sqrt{3}$

Answer 2

Let the ellipse be $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, since, y = x and

3y = -2x is a pair of conjugate diameters, therefore,

$m_{1}m_{2} = - \frac{b^{2}}{a^{2}}$ ⇒ 1. $\left( - \frac{2}{3} \right)$= $\sqrt{\frac{5}{2}}$ ⇒ 2a² = 3b²

⇒ 2a² = 3a²(1-e²) ⇒ e² = 1/3 ⇒ e = 1/$\sqrt{3}$.