Answer
$${y^2} = \frac{{25}}{2}x$$
Work Step by Step
$$\eqalign{
& {\text{through the point }}\left( {2,5} \right),{\text{ opens right}} \cr
& {\text{The equation opens rigth}},{\text{ then the equation is of the form }} \cr
& {y^2} = 4px,\,\,\,p > 0 \cr
& {\text{We know the point }}\left( {2,5} \right) \cr
& {\left( 5 \right)^2} = 4p\left( 2 \right) \cr
& 25 = 8p \cr
& p = \frac{{25}}{8} \cr
& {\text{,then}} \cr
& {y^2} = 4\left( {\frac{{25}}{8}} \right)x \cr
& {y^2} = \frac{{25}}{2}x \cr} $$
