Question

If an ellipse the distance between the foci is 8 and the distance between the directrices is 25. The length of the minor axis is

• A. $10\sqrt{2}$
• B. $20\sqrt{2}$
• C. $30\sqrt{2}$
• D. none of these.

Answer 1

Answer: (A)

$10\sqrt{2}$

Answer 2

Let the ellipse be $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1$ Distance between foci $= 2ae = 8$ $\Rightarrow ae = 4$ Distance between directrices $= \frac{2a}{e} = 25$ $\therefore \left(ar\right)\left(\frac{2a}{e}\right) = 4\times25$ $\Rightarrow 2a^{2} = 100$ $\Rightarrow a^{2} = 50$ $\Rightarrow a= 5\sqrt{2}$ $\Rightarrow 2a= 15\sqrt{2}$ $\therefore$ length of major axis $= 10\sqrt{2}$