Question

How do you write the standard form of a parabola with the vertex and focus?

Answer 1

The standard form of the equation of the parabola, If it has a vertical axis is given as:

${(x-h)}^2=4p(y-k)$, where $p\ne 0$.

The vertex of this parabola is at $(h,k)$.

The focus is at $(h,k+p)$.

The directrix is the line $y=k-p$.

Hence, we can write the standard form of a parabola as ${\mathbf{(}\mathit{x}\mathbf{}\mathbf{-}\mathbf{}\mathit{h}\mathbf{)}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathit{p}\mathbf{(}\mathit{y}\mathbf{}\mathbf{-}\mathbf{}\mathit{k}\mathbf{)}$