In an ellipse, distance between its foci is 6 and minor axis is 8 . Then its eccentricity is

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10-2. Parabola, Ellipse, Hyperbola

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In an ellipse, the distance between its foci is $6$ and minor axis is $8$. Then its eccentricity is

A

$\frac{4}{5}$

B

$\frac{1}{2}$

C

$\frac{3}{5}$

D

$\frac{1}{{\sqrt 5 }}$

(AIEEE-2006)

Solution

$2 a e=6 \Rightarrow a e=3 ; 2 b=8 \Rightarrow b=4$

$b^{2}=a^{2}\left(1-e^{2}\right) ; 16=a^{2}-a^{2} e^{2}$

$\Rightarrow a^{2}=16+9=25$

$\Rightarrow a=5$

$\therefore e=\frac{3}{a}=\frac{3}{5}$

Standard 11

Mathematics

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