Answer
$y^{2}= 16x$
Work Step by Step
Given: The parabola $y^{2}= 4px$ with directrix $x=-p$ such that $p^2=16$
This implies that $p=4, p \gt 0$
The equation of directrix shows that this parabola opens to the right.
so, the general form of the equation of a parabola which opens to the right is
$y^{2}= 4px$
Thus, the equation of the parabola becomes:
$y^{2}= 4(4)x$
$\implies y^{2}= 16x$
