Tangents are drawn to the hyperbola x^ 2 9 - y^ 2 4 =1 , parallel...

If slope of tangents to hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is $m$, then equations of tangent to the hyperbola is $y=m x \pm \sqrt{a^{2} m^{2}-b^{2}} \quad$ with the points of contact $\quad\left(\quad \pm a^{2} m\right. \left.\frac{\pm \sqrt{a^{2} m^{2}-b^{2}}}{\sqrt{a^{2} m^{2}-b^{2}}}\right) \therefore$ Tangent to hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ is parallel to $2 x-y=1$, $\therefore$ Slope of tangent $=2 \therefore$ Points of contact are \left(\frac{\pm 9 \times 2}{\sqrt{9 \times 4-4}}, \frac{\pm 4}{\sqrt{9 \times 4-4}}\right)$i.e.$\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$and \left(\frac{-9}{2 \sqrt{2}}, \frac{-1}{\sqrt{2}}\right)$