Equation of ellipse whose distance between foci is equal to 8 and distance between directrix is 18 ,

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10-2. Parabola, Ellipse, Hyperbola

easy

The equation of ellipse whose distance between the foci is equal to $8$ and distance between the directrix is $18$, is

A

$5{x^2} - 9{y^2} = 180$

B

$9{x^2} + 5{y^2} = 180$

C

${x^2} + 9{y^2} = 180$

D

$5{x^2} + 9{y^2} = 180$

Solution

(d) $2ae = 8,\,\,\frac{{2a}}{e} = 18$ $⇒$ $a = \sqrt {4 \times 9} = 6$

$e = \frac{2}{3},$ $b = 6\sqrt {1 – \frac{4}{9}} = \frac{6}{3}\sqrt 5 = 2\sqrt 5 $

Hence the required equation is $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{20}} = 1$

$i.e.$, $5{x^2} + 9{y^2} = 180$.

Standard 11

Mathematics

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