Question

If e^­₁ and e₂ are the eccentricities of the conic sections 16x² + 9y² = 144 and 9x² – 16y² = 144, then-

• A. $e_{1}^{2} + e_{2}^{2} = 3$
• B. $e_{1}^{2} + e_{2}^{2} > 3$
• C. $e_{1}^{2} + e_{2}^{2} < 3$
• D. $e_{1}^{2} - e_{2}^{2} > 1$

Answer 1

Answer: (C)

$e_{1}^{2} + e_{2}^{2} < 3$

Answer 2

16x² + 9y² = 144 9x² – 16y² = 144

$\frac{x^{2}}{9}$ + $\frac{y^{2}}{16}$ = 1 $\frac{x^{2}}{16}$ – $\frac{y^{2}}{9}$ = 1

e₁ = $\sqrt{1 - \frac{9}{16}}$ e₂ = $\sqrt{1 + \frac{9}{16}}$

e₁ = $\frac{\sqrt{7}}{4}$ e₂ = $\frac{5}{4}$

e₁² + e₂² = $\frac{7}{16}$ + $\frac{25}{16}$ = $\frac{32}{16}$ = 2