Mathematics - Straight line Question with Solution | TestHub

$\begin{array}{rl}& \left({\mathrm{x}}^2+2\mathrm{x}\right)(12-\mathrm{k})=2\\ & \lambda {\mathrm{x}}^2+2\lambda \mathrm{x}-2=0\mathrm{k}\ne 12\text{ Let }12-\mathrm{k}=\lambda \\ & \mathrm{D}=0\\ & 4{\lambda }^2+8\lambda =0\\ & \lambda =0\text{ or }\lambda =-2\\ & \Rightarrow 12-\mathrm{k}=-2\\ & \mathrm{k}=14\end{array}$
$\text{ So }P\left(k,\frac{k}{2}\right)=(14,7)$
$\mathrm{d}=\left|\frac{3\times 14+4\times 7+5}{5}\right|=15$
option (1)