Answer
$x^2=10y$
Work Step by Step
Equation of a parabola with vertical axis: $x^2=4py$
The parabola passes through the point $(5,p)$. Let' use the point $(5,p)$:
$5^2=4p(p)$
$25=4p^2$
$p^2=\frac{25}{4}$
$p=±\frac{5}{2}$
The parabola opens upwards. Focus is on the positive y-axis. So, $p$ is also positive:
$p=\frac{5}{2}$
$x^2=4py$
$x^2=4(\frac{5}{2})y$
$x^2=10x$
