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
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
Updated On: Dec 25, 2023
- $10\sqrt{2}$
- $20\sqrt{2}$
- $30\sqrt{2}$
- none of these.
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The Correct Option is A
Solution and Explanation
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 $= 10\sqrt{2}$
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