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 \((0,~2)\) and directrix \(y~=~-2\), 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.
A parabola’s main features come from one perpendicular focus-to-directrix construction. We’ll project the focus onto the line, take the midpoint for the vertex, use the perpendicular orientation for the axis, read signed p toward the focus, infer the opening, and confirm equal defining distances at the vertex.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
