Equations of the asymptotes of the hyperbola $3x^2+10xy+8y^2+14x+22y+7=0$ is.

 

Since the equation of a hyperbola differs from  the combined equation of the asymptotes by a constant. Let the equation of the asymptotes be

$3x^2+10xy+8y^2+14x+22y+\lambda =0$

This will represent a pair of straight lines if 

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

where $\begin{array}{l}a=3,b=8,c=\lambda ,f=11,g=7,h=5\\ 3\times 8\times \lambda +2\times 11\times 7\times 5-3\times 121-8\times 49 -\lambda \left(25\right)=0\\ \lambda =25\end{array}$