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10-2. Parabola, Ellipse, Hyperbola
easy
If the eccentricity of an ellipse be $5/8$ and the distance between its foci be $10$, then its latus rectum is
A
$39/4$
B
$12$
C
$15$
D
$37/2$
Solution
(a) $a = \frac{{10}}{{\frac{{2.5}}{8}}} = 8$, $b = 8\sqrt {1 – \frac{{25}}{{64}}} = 8\frac{{\sqrt {39} }}{8}$ = $\sqrt {39} $
Latus rectum$ = \frac{{2{b^2}}}{a} = \frac{{2 \times 39}}{8} = \frac{{39}}{4}$.
Standard 11
Mathematics