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)

$\sqrt{6/7}$

Answer 2

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