- Home
- Standard 11
- Mathematics
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
Similar Questions
normal