# Find the length of the latus rectum of the hyperbola x2 - 2y2 = 4 ?

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Find the length of the latus rectum of the hyperbola x2 - 2y2 = 4 ?
1. 2
2. 1
3. $\sqrt 2$
4. None of these.
5. 3

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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.