Mathematics - Ellipse Question with Solution | TestHub

Given equation of parabola is $y^2-kx+6=0$ $\Rightarrow y^2=kx-6\Rightarrow y^2=k\left(x-\frac{6}{k}\right)$ Now, directrix, $x-\frac{6}{k}=-\frac{k}{4}$ $\Rightarrow x=\frac{6}{k}-\frac{k}{4}$ ...(i) But directrix is given $\Rightarrow x=\frac{1}{2}$ ...(ii) $\begin{array}{rl}& \therefore \frac{6}{k}-\frac{k}{4}=\frac{1}{2}\Rightarrow 24-k^2=2k\\ & \Rightarrow k^2+2k-24=0\\ & \Rightarrow (k+6)(k-4)=0\Rightarrow k=-6,k=4\end{array}$