Question

Let a hyperbola be \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and ellipse be \(\frac{x^2}{9} + \frac{y^2}{8} = 1\). If length of latus rectum of hyperbola is equal to minor axis of ellipse and eccentricity of hyperbola is equal to semi-major axis of ellipse, then \(2ae\) is equal to (where 'e' is the eccentricity of hyperbola)

• A. \(3\sqrt{2}\)
• B. \(\frac{3\sqrt{2}}{2}\)
• C. \(2\sqrt{2}\)
• D. \(\frac{\sqrt{2}}{3}\)

Hint:

For an ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), the semi-major axis is $a$ and the minor axis length is $2b$. Always be careful to distinguish between 'semi-axis' and 'axis length'.

Answer 1

The Correct Option is B