Question

Find the equation of the parabola with a vertex of (5, -2) and a focus of (5, -3)

Answer 1

Use the form $\left(x-h\right)^2=\frac{1}{4p}\left(y-k \right)$
Then we have the vertex is $(h,k)$ and the distance from the vertex to the focus is p. Therefore we have $\left(x-5\right)^2=-\frac{1}{4}\left(y+2\right)$. It is negative because the parabola is pointing downwards.