Question

If the semi-major axis of an ellipse is 3 and the latus rectum is 16/9, then the standard equation of the ellipse is

• A. $\frac{x^2}{9}+\frac{y^2}{8}=1$
• B. $\frac{x^2}{9}+\frac{3y^2}{8}=1$
• C. $\frac{x^2}{9}+\frac{8y^2}{3}=1$
• D. $\frac{x^2}{3}+\frac{y^2}{8}=1$

Answer 1

The correct option is B

$\frac{x^2}{9}+\frac{3y^2}{8}=1$

Given that a = 3
$LatusRectum=\frac{2b^2}{a}=\frac{16}{9}\frac{2}{3}{b}^2=\frac{16}{9}{b}^2=\frac{8}{3}$

The standard equation of the ellipse is

$\frac{x^2}{9}+\frac{3y^2}{8}=1$