For the hyperbola $x^{2} - y^{2} - 2 x - 2 y = 4$ , which of the following is/are true

length of conjuage axis is

4

unit

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centre is

(1, - 1)

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eccentricity is

\sqrt{2}

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length is latus rectum is

4

unit

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Solution

The correct option is D length is latus rectum is $4$ unit
Gievn hyperbola is $x^{2} - y^{2} - 2 x - 2 y = 4$
$\Rightarrow \frac{(x - 1)^{2}}{4} - \frac{(y + 1)^{2}}{4} = 1$
$\Rightarrow a = b = 2$ unit, it's a rectangular hyperbola
So, $e = \sqrt{2}$
and centre is $(1, - 1)$
length of latus rectum is $\frac{2 b^{2}}{a}$
$= \frac{2 \times 2^{2}}{2}$
$= 4$ unit

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