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G-GPE.2 Warmup M2-042-A02-V03

Derive the equation of a parabola from a focus and directrix.

Derive a vertical parabola equation from focus and directrix

Problem

Derive the equation of the parabola with focus \((-2,~-1)\) and directrix \(y~=~5\). Find the vertex midpoint and signed \(p\), identify the vertical standard form, and substitute into \((x~-~h)^{2}~=~4p(y~-~k)\).

Coordinate plane with focus (−2,−1) and directrix y=5; vertex and parabola equation are not shown. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GPE.2
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Derive the equation of a parabola from a focus and directrix.
Problem type
Derive a vertical parabola equation from focus and directrix