Equations of tangents to the hyperbola $4{\mathrm{x}}^2 – 3{\mathrm{y}}^2 =24$ which makes an angle $30°$ with y-axis are

$$\begin{gathered} Given hyperbola \frac{{\mathrm{x}}^2}{6}-\frac{{\mathrm{y}}^2}{8}=1 \\ where {\mathrm{a}}^2=6, {\mathrm{b}}^2=8, \\ \mathrm{As} \mathrm{the} \mathrm{line} \mathrm{makes} \mathrm{an} \mathrm{angle} {30}^0 with y-axis, so \mathrm{slope} \mathrm{of} \mathrm{tangen}t( \mathrm{m})=\tan {60}^0=\sqrt{3} \\ \mathrm{Now} \mathrm{equation} \mathrm{of} \mathrm{tangent} \mathrm{is} \mathrm{y}=\mathrm{mx}\pm \sqrt{{\mathrm{a}}^2{\mathrm{m}}^2-{\mathrm{b}}^2} \\ \mathrm{y}=\sqrt{3}\mathrm{x}\pm \sqrt{18-8} \\ \Rightarrow \sqrt{3}\mathrm{x}-\mathrm{y}=\pm \sqrt{10} \end{gathered}$$