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

Question

Question

Answer 1

Concept:

The length of the latus rectum of the ellipse \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is equal to \(\rm \frac{2a^2}{b}\). (a < b)

Calculation:

Writing the equation of the ellipse in the standard form \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), we get:

\(\rm \frac{x^2}{2^2}+\frac{y^2}{(2\sqrt3)^2}=1\)

∴ a = 2 and b = 2√3.

Here a < b

Length of the latus rectum = \(\rm \frac{2a^2}{b}\) = \(\rm \frac{2(2^2)}{2\sqrt3}\) = \(\rm \frac{4}{\sqrt3}\).