Question

In an ellipse, the distance between the foci is 8 and the distance between the directrices is 25. Then the length of major axis is

• A. 10$\sqrt{2}$
• B. 20$\sqrt{2}$
• C. 30$\sqrt{2}$
• D. 40$\sqrt{2}$

Answer 1

Answer: (A)

10$\sqrt{2}$

Answer 2

Given 2ae = 8 ⇒ ae = 4 ... (1)

$\frac{\mathbf{2a}}{\mathbf{e}}\mathbf{= 25}$⇒ a/e = $\frac{25}{2}$ .......(2)

(1) x (2) ⇒ a² = 50

∴ a = $\sqrt{50}$

∴ length of major axis = 2a = $10\sqrt{2}$