The equation of the asymptotes of the hyperbola $2x^2+5xy+2y^2-11x-7y-4=0$ is

The equation of hyperbola is $2x^2+5xy+2y^2-11x-7y-4=0......\left(1\right)$

Let asymptotes of the hyperbola (1) be $2x^2+5xy+2y^2-11x-7y+c=0......\left(2\right)$

Since, Eq (2) represent pair of lines

$\therefore \left|\begin{array}{ccc}2& 5/2& -11/2\\ 5/2& 2& -7/2\\ -11/2& -7/2& c\end{array}\right|=0$

$\Rightarrow -\frac{11}{2}\left(-\frac{35}{4}+11\right)+\frac{7}{2}\left(-7+\frac{55}{4}\right)+c\left(4-\frac{25}{4}\right)=0$

$\Rightarrow \frac{9}{4}c=-\frac{99}{8}+\frac{189}{8}=\frac{90}{8}\Rightarrow c=5$

$\therefore$ equation of the required asymptotes is

$2x^2+5xy+2y^2-11x-7y+5=0$