Mathematics - Parabola Question with Solution | TestHub

$y^2=8k,xy=-1$ Let $P\left(t,\frac{-1}{t}\right)$ be any point on $\mathrm{xy}=-1$ Equation of the tangent to $xy=-1$ at $P\left(t,\frac{-1}{t}\right)$ is $\begin{array}{rlrl}& \frac{x{y}_1+y{x}_1}{2}=-1& \frac{-x}{t}+yt=-2& y=\frac{x}{t^2}+\left(\frac{-2}{t}\right).\end{array}$ If (1) is tangent to the parabola $y^2=8x$ then $\begin{array}{rlr}& \frac{-2}{t}=\frac{2}{1/t^2}\Rightarrow t^3=-1& t=-1\end{array}$ ∴ Common tangent is $\mathrm{y}=\mathrm{x}+2$