For what value of $\lambda$ does the line $y=2x+\lambda$ touches the hyperbola $16x^2-9y^2=144$?

Question

$\begin{array}{1 1}(a)\;\pm 2\sqrt 5\\(b)\;\pm 2\sqrt 7\\(c)\;\pm 3\sqrt 5\\(d)\;\pm 4\sqrt 5\end{array}$