Question

The eccentricity of the conic $3x^2 + 4y^2 = 24$ is

• A. $\frac{1}{4}$
• B. $\frac{7}{4}$
• C. $\frac{1}{2}$
• D. $\sqrt{\frac{7}{4}}$

Answer 1

Answer: (C)

$\frac{1}{2}$

Answer 2

Given ellipse is $\frac{x^{2}}{8}+\frac{y^{2}}{6}= 1$
Here $a^{2} = 8, b^{2}= 6 ;$ Since $b^{2}= a^{2}\left(1-e^{2}\right)$
$\therefore 6= 8\left(1-e^{2}\right)$
$\Rightarrow 1-e^{2} = \frac{3}{4}$
$\Rightarrow e^{2}= \frac{1}{4}$
$\Rightarrow e=\frac{1}{2}$