Question

Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.

Answer 1

Answer on Question #45101 – Math – Analytic Geometry

Find the standard form of the equation of the parabola with a focus at $(0,2)$ and a directrix at $y = -2$.

Distance $p$ between directrix and focus is $2 - (-2) = 4$. Due to the fact that directrix is parallel to the axis $Ox$, we can say that the standard form of a parabola's equation is

$$x^{2} = 2py.$$

So, the answer is the following:

$$x^{2} = 8y$$

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