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  4. If e1 and e2 are the eccentricities of the conic sections 16 x2+9 y2=144 and 9 x2-16 y2=144, then

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Q. If $e_1$ and $e_2$ are the eccentricities of the conic sections $16 x^2+9 y^2=144$ and $9 x^2-16 y^2=144$, then

Conic Sections

Solution:

$e _1^2=1-\frac{144}{16} \times \frac{9}{144}=\frac{7}{16} $
$e _2^2=1+\frac{44}{16} \times \frac{9}{144}=\frac{25}{16} $
$\Rightarrow e _1^2+ e _2^2=2$