# The line $4x+2y=c$ is a tangent to the parabola $y^{2}=16x$ then $c$ is

$\begin{array}{1 1}(1)-1&(2)-2\\(3)4&(4)-4\end{array}$

$y^2=16x$
$y^2=4(4)x => a=4$
$4x+2y=c=> 2y=-4x+c$
$y= -\large\frac{4}{2}x + \frac{c}{2}$
$y= -2x+\large\frac{c}{2}$
Comparing with the equitation $y= mx+c$
$m= -2, c= \large\frac{c}{2}$
$\large\frac{c}{2} =\frac{4}{-2}$
$c= -4$
Hence 4 is the correct answer.