Derive the equation of a parabola from a focus and directrix.
Find the vertex of a parabola from focus and directrix
Problem
Find the vertex of the parabola with focus \((0,2)\) and directrix \(y=-2\).
Big Picture
What this problem is really about
The vertex is not the focus; it is the balance point between the focus and directrix. We’ll project the focus perpendicularly onto the line, take the midpoint of that segment coordinate by coordinate, and verify that the resulting point has equal focus distance and perpendicular directrix distance.
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