Question

Find the length of the latus rectum of the hyperbola x2 - 2y2 = 4 ?
1. 2
2. 1
3. \(\sqrt 2\)
4. None of these.

Answer 1

Correct Answer - Option 1 : 2

Concept:

In a hyperbola \(\rm \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), a > b:

The length of the latus rectum is equal to \(\rm \frac{2b^2}{a}\).

 

Calculation:

The given equation of the hyperbola can be written as:

\(\rm \frac{x^2}{2^2}-\frac{y^2}{\left(\sqrt2\right)^2}=1\)

Here, b² = 2 and a = 2.

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