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

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

Conic Sections

Solution:

According to given condition, $2 a e=8, \frac{2 a}{e}=18$
$\Rightarrow a=\sqrt{4 \times 9}=6$
$\Rightarrow e=\frac{2}{3}, b=6 \sqrt{1-\frac{4}{9}}=\frac{6}{3} \sqrt{5}=2 \sqrt{5}$
Hence, the required equation is $\frac{x^2}{36}+\frac{y^2}{20}=1$
i.e., $ 5 x^2+9 y^2=180$