Question

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

• A. length of conjuage axis is $4$ unit
• B. centre is $(1,-1)$
• C. eccentricity is $\sqrt{2}$
• D. length is latus rectum is $4$ unit

Answer 1

Answer: (A), (B), (C), (D)

length is latus rectum is $4$ unit

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