Answer
$(x-4)^2=8(y-3)$
Work Step by Step
Because the vertex and the focus have the same $x$-coordinate, it follows that the parabola has a vertical axis of symmetry.
Since the focus is above the vertex and the axis of symmetry is vertical, it means that the parabola opens upward.
The standard form of a vertical parabola is given as: $(x-h)^2=4p(y-k) ~~~(1)$
The directed distance (p) between the vertex and the focus is $p=5-3=2$
Here, we have $h=4; k =3$
Now, we will plug these values in equation (1) to obtain:
$(x-4)^2=4 (2)(y-3) \implies (x-4)^2=8(y-3)$
