If the line $y=\sqrt 3x+k$ touches the circle $x^2+y^2=16$,then find the value of $k$.

Question

[Hint: Equate perpendicular distance from the centre of the circle to its radius].

$\begin{array}{1 1}k=8\\k=\pm 9\\k=\pm 8\\k=-9\\\end{array}$