Find the equation of a parabola that satisfies the following condition - vertex $(0,0)$ and passing through $(5,2)$ and symmetric with respect to y-axis.

Question

$\begin{array}{1 1} x^2= \frac{25}{2} y \\y^2= \frac{25}{8} x \\x^2= \frac{-25}{4} y \\ y^2= \frac{-25}{16} x \end{array}$