Mathematics - Hyperbola Question with Solution | TestHub

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 $y=mx\pm \sqrt{a^2{m}^2-b^2}$ with the points of contact $(\pm a^{2}m$ $\frac{\pm \sqrt{a^2{m}^2-b^2}}{\sqrt{a^2{m}^2-b^2}})$ $\therefore$ Tangent to hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ is parallel to $2x-y=1$, $\therefore$ 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 $\left(\frac{-9}{2\sqrt{2}},\frac{-1}{\sqrt{2}}\right)$