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G-GPE.2 Warmup M2-042-A01-V04

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

Derive separate parabola features from focus and directrix

Problem

For a parabola with focus \((-4,~2)\) and directrix \(x~=~0\), project the focus perpendicularly to the directrix and take the midpoint for the vertex. Report the axis, signed focal parameter \(p\), opening direction, and equal-distance check.

Coordinate plane with focus (−4,2) and vertical directrix x=0; vertex, axis, p-value, and parabola 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 separate parabola features from focus and directrix