The equation of the ellipse whose latus rectum is 8 and whose ecc… - Vidyadip

MCQ

The equation of the ellipse whose latus rectum is $8$ and whose eccentricity is $\frac{1}{{\sqrt 2 }}$, referred to the principal axes of coordinates, is

A
$\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$
B
$\frac{{{x^2}}}{8} + \frac{{{y^2}}}{9} = 1$
✓
$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{32}} = 1$
D
$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{24}} = 1$

✓

Answer

Correct option: C.

$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{32}} = 1$

c
(c) $\frac{{2{b^2}}}{a} = 8,$$e = \frac{1}{{\sqrt 2 }}$

${a^2} = 64,\,{b^2} = 32$

Hence required equation of ellipse is

$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{32}} = 1$.

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