If distance between a focus and corresponding directrix of an ellipse be 8 and eccentricity be 1/2 ,

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10-2. Parabola, Ellipse, Hyperbola

easy

If the distance between a focus and corresponding directrix of an ellipse be $8$ and the eccentricity be $1/2$, then length of the minor axis is

A

$3$

B

$4\sqrt 2 $

C

$6$

D

None of these

Solution

(d) $\frac{a}{e} – ae = 8$. Also $e = \frac{1}{2}$

$a = \frac{{8e}}{{(1 – {e^2})}} = \frac{{8.4}}{{2(3)}} = \frac{{16}}{3}$

$\therefore b = \frac{{16}}{3}\sqrt {\left( {1 – \frac{1}{4}} \right)} = \frac{{16}}{3}\frac{{\sqrt 3 }}{2} = \frac{{8\sqrt 3 }}{3}$

Hence the length of minor axis is $\frac{{16\sqrt 3 }}{3}$.

Standard 11

Mathematics

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