Question

The eccentricity of an ellipse is $\frac{2}{3}$ , latus rectum is 5 and centre is (0, 0). The equation of the ellipse is

• A. $\frac{4x^2}{81}+\frac{y^2}{45}=1$
• B. $\frac{4x^2}{81}+\frac{4y^2}{45}=1$
• C. $\frac{x^2}{9}+\frac{y^2}{5}=1$
• D. $\frac{x^2}{81}+\frac{y^2}{45}=5$

Answer 1

The correct option is B

$\frac{4x^2}{81}+\frac{4y^2}{45}=1$

${\left(\frac{2}{3}\right)}^2=1-\frac{b^2}{a^2}and\frac{2b^2}{a}=5\Rightarrow a^2=\frac{81}{4},b=\frac{45}{4}$

Hence the equation is $\frac{4x^2}{81}+\frac{4y^2}{45}=1$