Question

Eccentricity of ellipse $\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1 $ if it passes through point $(9, 5)$ and $(12, 4)$ is

• A. $\sqrt{3/4} $
• B. $\sqrt{4/5} $
• C. $\sqrt{5/6} $
• D. $\sqrt{6/7} $

Answer 1

Answer: (D)

We have $\frac{81}{a^{2}} + \frac{25}{b^{2}} = 1$ ......(1)
$ \frac{144}{a^{2}} + \frac{16}{b^{2}} = 1 $ .......(2)
From eq. (2) - eq. (1) :
$\frac{63}{a^{2}} - \frac{9}{b^{2}} = 0$
$ \Rightarrow \frac{b^{2}}{a^{2}} = \frac{1}{7} $
$ e = \sqrt{1- \frac{1}{7}} = \sqrt{\frac{6}{7}} $