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The distance between the foci of the ellipse $9x^{2}+5y^{2}=180 $ is

\[\begin{array}{1 1}(1)4&(2)6\\(3)8&(4)2\end{array}\]

1 Answer

$9x^2+5y^2=180$
$\large\frac{9x^2}{180} +\frac{5y^2}{180}$$=1$
$\large\frac{x^2}{20} +\frac{y^2}{36}$$=0$
$a^2=36$
$b^2=20$
$e= \sqrt {1- \large\frac{^2}{a^2}}$
$\quad= \sqrt { \large\frac{16}{36}}$
$\quad=\large\frac{4}{9}$
$e=\large\frac{2}{3}$
Distance between the foci $=2ae$
$\quad= 2 \times 6 \times \large\frac{2}{3}$$=8$
Hence 3 is the correct answer
answered May 16, 2014 by meena.p
 

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