Statement-I : The combined equation of the pair of asymptotes of the hyperbola $2\mathrm{xy} + 6\mathrm{x} + \mathrm{y} + 5 = 0$ is $2\mathrm{xy} + 6\mathrm{x} + \mathrm{y} + 3 = 0$
Statement-II : The angle between the asympotes of the hyperbola $\mathrm{xy}–2\mathrm{y}+3\mathrm{x}+ \sqrt{3}=0$ is ${60}^0$ . Which of above statements is true

$$\begin{gathered} \underline{\mathrm{Statement}-\mathrm{I}} : \mathrm{Given} \mathrm{hyperbola} S\equiv 2\mathrm{xy}+6\mathrm{x}+\mathrm{y}+5=0 \\ Now \frac{\partial S}{\partial x}=0\Rightarrow 2y+6=0\Rightarrow y=-3 and \\ \frac{\partial S}{\partial y}=0\Rightarrow 2x+1=0\Rightarrow x=\frac{-1}{2} \\ \therefore \mathrm{centre}\left(\mathrm{c}\right)=\left(\frac{-1}{2}, -3\right) \\ Now e\mathrm{quation} \mathrm{of} \mathrm{pair} \mathrm{of} \mathrm{asymptotes} \mathrm{is} 2\mathrm{xy}+6\mathrm{x}+\mathrm{y}+\mathrm{k}=0 \\ \sin ce asymptotes passes through centre \left(\frac{-1}{2}, -3\right) then \\ \Rightarrow \mathrm{k}=3 \\ \therefore \mathrm{pair} \mathrm{of} \mathrm{asymptotes} \mathrm{is} 2\mathrm{xy}+6\mathrm{x}+\mathrm{y}+3=0 \\ \mathrm{Statement} \mathrm{I} \mathrm{is} \mathrm{true} \end{gathered}$$

$$\begin{gathered} \underline{\mathrm{Statemnet}-\mathrm{II}} : \\ \mathrm{Given} \mathrm{hyperbola} \mathrm{xy}-2\mathrm{y}+3\mathrm{x}+\sqrt{3}=0 \\ \mathrm{Equation} \mathrm{of} \mathrm{pair} \mathrm{of} \mathrm{asymptotes} \mathrm{xy}-2\mathrm{y}+3\mathrm{x}+\mathrm{k}=0 \\ \Rightarrow \mathrm{a}+\mathrm{b}=0 \\ \therefore \mathrm{Asymptotes} \mathrm{are} \mathrm{perpendiculer} \mathrm{to} \mathrm{each} \mathrm{other} \\ So,given hyperbola is rec\tan gular hyperbola \\ \therefore Angle between asymptotes\left(\mathrm{\theta }\right)={90}^0 \\ \therefore \mathrm{Statement} \mathrm{II} \mathrm{is} \mathrm{wrong} \end{gathered}$$