The combined equation of the asymptotes of the hyperbola $2x^2+5xy+2y^2+4x+5y=0,$ is

Let the equations of asymptotes be 

$2x^2+5xy+2y^2+4x+5y+\lambda =0$                 …(i)

This equation represents a pair of straight lines. Therefore,

$abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$

Here, $a=2,b=2,h=5/2,g=2,f=5/2$ and $c=\lambda$

$\therefore 4\lambda +25-\frac{25}{2}-8-\frac{25}{4}\lambda =0\Rightarrow -\frac{9\lambda }{4}+\frac{9}{2}=0\Rightarrow \lambda =2$

Putting the value of $\lambda$ in (i), we get

$2x^2+5xy+2y^2+4x+5y+2=0$

This is the equation of the asymptotes.