If distance between foci of an ellipse be equal to its minor axis, then its eccentricity is

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10-2. Parabola, Ellipse, Hyperbola

easy

If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is

A

$1\over2$

B

$1\over\sqrt 2 $

C

$1\over3$

D

$1\over\sqrt 3 $

Solution

(b) Foci are $( \pm ae,0)$.

Therefore according to the condition, $2ae = 2b$ or $ae = b$

Also, ${b^2} = {a^2}(1 – {e^2})$

${e^2} = (1 – {e^2})$==> $e = \frac{1}{{\sqrt 2 }}$.

Standard 11

Mathematics

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