Question

The eccentricity of ellipse $4x^2+9y^2=36$ is

• A. $\frac{1}{2\sqrt{3}}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{\sqrt{5}}{3}$
• D. $\frac{\sqrt{5}}{6}$

Answer 1

Answer: (C)

$\frac{\sqrt{5}}{3}$

first write the equation of ellipse in correct format

i.e.

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

hence we will get

eccentricity is given by

$e=\sqrt{1-\frac{b^2}{a^2}}$

$\sqrt{1-\frac{2^2}{3^2}}=e\frac{\sqrt{5}}{3}=e$