Question

If the rectangular hyperbola is $x^2-y^2=64$. Then, which of the following is not correct?

• A. The length of latus rectum is $16$
• B. The eccentricity is $\sqrt{2}$
• C. The asymptotes are parallel to each other
• D. The directrices are $x=\pm 4\sqrt{2}$

Answer 1

Answer: (C)

The asymptotes are parallel to each other

Given equation of rectangular hyperbola is $x^2-y^2=8^2$

Here, $a=8$ and $b=a$
Length of latus rectum $=2\times \frac{b^2}{a}=2\times \left(8\right)=16$
and eccentricity $=\sqrt{2}$
The asymptotes are perpendicular lines.
So, $x\pm y=0$
Now, directrices are
$x=\pm \frac{8}{\sqrt{2}}=\pm 4\sqrt{2}$

Hence, statement given in C is not correct.