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

The asymptotes of a rectangular hyperbola are perpendicular to each other. Given one asymptote, x + y + c=0. 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 asymptote must be concurrent. Thus, we have
$\begin{array}{l}\left|\begin{array}{l}2-10\\ 11c\\ 1-1\lambda \end{array}\right|=0\\ \Rightarrow \lambda =-3c\end{array}$