Question

The length of the latus rectum of the ellipse 3x² + y² = 12 is ______.

Options

• 4

• 3

• 8

• ${\displaystyle \frac{4}{\sqrt{3}}}$

Answer 1

The length of the latus rectum of the ellipse 3x² + y² = 12 is ${\displaystyle \frac{4}{\sqrt{3}}}$.

Explanation:

Equation of the ellipse is 3x² + y² = 12

⇒ ${\displaystyle \frac{x^2}{4}+\frac{y^2}{12}}$ = 1

Here a² = 4 ⇒ a = 2

b² = 12 ⇒ b = ${\displaystyle 2\sqrt{3}}$

Length of the latus rectum = ${\displaystyle \frac{2a^2}{b}=\frac{2\times 4}{2\sqrt{3}}=\frac{4}{\sqrt{3}}}$