Question

If the focus and vertex of a parabola are the points $(0,2)$ and $(0,4)$, respectively. then find its equation.

Answer 1

Shifting origin to vector of parabola $(0,4),X=x,Y=y-4$

$\Rightarrow$ focus at $(0,-2)\Rightarrow a=2$ (distance between focus and vector)

and axis is along negative y-axis

$\Rightarrow X^2=-4\left(2\right)y\Rightarrow X^2=-8y\Rightarrow x^2=-8(y-4)$ is required equation