Question

Find the equation of parabola with vertex $(0,0)$ & focus at $(0,2)$.

Answer 1

Given the vertex of the parabola is $(0,0)$ and focus is at $(0,2)$.

This gives the axis of the parabola is the positive $y-$ axis.

Then the equation of the parabola will be $x^2=4ay$ where $a=2$.

So the equation of the parabola is $x^2=8y$.