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) :
$\frac{63}{a^2}-\frac{9}{b^2}=0$
$\Rightarrow \frac{b^2}{a^2}=\frac{1}{7}$
$e=\sqrt{1-\frac{1}{7}}=\sqrt{\frac{6}{7}}$