Derive the equation of a parabola from a focus and directrix.
Read separate focus and directrix fields from a parabola equation
Problem
Identify focus and directrix from \(x^{2}=8y\).
Big Picture
What this problem is really about
Reading a parabola equation backward starts by matching its orientation and shifts to standard form. We’ll identify the vertex, solve the unsquared-coordinate coefficient as four times p, move from the vertex by signed p to locate the focus, place the directrix the same distance oppositely, and check the opening.
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