Question

The centre of a rectangular hyperbola lies on the line $y=2x$. If one of the asymptotes is $x+y+c=0$, then the other asymptote is

• A. $3x-3y-c=0$
• B. $2x-y+c=0$
• C. $x-y-c=0$
• D. None of these

Answer 1

The correct option is A $3x-3y-c=0$

Given one asymptote,
$x+y+c=0$
The asymptotes of a rectangular hyperbola are perpendicular to each other.
So, let the other asymptote be
$x-y+\lambda =0$
We also know that the asymptotes pass through centre of the hyperbola. Therefore, the line $2x-y=0$ and the asymptotes must be concurrent.
Thus, we have
$\left|\begin{array}{ccc}2& -1& 0\\ 1& 1& c\\ 1& -1& \lambda \end{array}\right|=0$
$\Rightarrow 3\lambda =-c$
So, the equation of the asymptote will be $3x-3y-c=0$