Answer
$x^2=-4\sqrt 2y$
Work Step by Step
Equation of a parabola with vertical axis (vertex at origin): $x^2=4py$
Focus: $(0,p)$
When $y=p$:
$x^2=4pp=4p^2$
$x=±2p$
Rectangle:
$Width=p$
$Length=2p-(-2p)=4p$
$Area=8$
$p(4p)=8$
$p^2=2$
$p=±\sqrt 2$
We use: $p=-\sqrt 2$ because the parabola opens downwards.
$x^2=-4\sqrt 2y$
