Question

If e1 is the eccentricity of the conic 9x2 + 4y2 = 36 and e2 is the eccentricity of the conic 9x2 – 4y2 = 36, then-

• A. e12 + e22 = 2
• B. e12 + e22> 3
• C. e12 + e22< 2
• D. e12 + e22> 4

Answer 1

Answer: (B)

e12 + e22> 3

Answer 2

The equations in the standard form are $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ and $\frac{x^{2}}{4}–\frac{y^{2}}{9} = 1$

$e_{1}^{2} = \frac{9–4}{9} = \frac{5}{9},e_{2}^{2} = \frac{4 + 9}{4} = \frac{13}{4}$ and $e_{1}^{2}$+ $e_{2}^{2}$

= $\frac{137}{36}$ > 3 but < 4.