Problem preview
G-GPE.2 Warmup M2-042-A07-V01

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

Verify whether a point lies on a parabola using focus and directrix

Problem

Determine whether point \((2,1/2)\) lies on the parabola with focus \((0,2)\) and directrix \(y=-2\).

Big Picture

What this problem is really about

Parabola membership is a balance between two specific distances. We’ll compute the point-to-focus distance with coordinate differences, find the shortest perpendicular distance to the directrix rather than a slanted one, compare the exact values, and use the corresponding standard equation as an independent substitution check.

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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
Verify whether a point lies on a parabola using focus and directrix