First slide

Hyperbola in conic sections

Question

If e₁, and e₂ are respectively the eccentricities of the conics $\frac{x^{2}}{25} - \frac{y^{2}}{11} = 1 and \frac{x^{2}}{16} + \frac{y^{2}}{7} = 1$ then e₁ e₂ is equal to

Easy

A

$\frac{10}{9}$
B

$\frac{4}{3}$
C

$\frac{9}{10}$
D

$\frac{8}{5}$

Solution

$e_{1} = \sqrt{\frac{25 + 11}{25}} = \frac{6}{5}, e_{2} = \sqrt{\frac{16 - 7}{16}} = \frac{3}{4}$
$\Rightarrow e_{1} e_{2} = \frac{6}{5} \times \frac{3}{4} = \frac{9}{10}$

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