Curriculum placement
Geometry. This describes the skill, not a learner estimate.
A parabola as points equally far from a focus and a line
Derive a parabola equation from equal focus and directrix distances
Problem types
- Parabolas from focus and directrix
- Derive a parabola's equation, line by line
- Check a derivation of a parabola's equation
- Use the focus-directrix rule at one point
- Find the vertex of a parabola from its directrix and the distance to its focus
Builds on
Leads to
- Conic sections and their equations · Extend the idea
A parabola is the points equally far from a focus and a directrix. Ellipses and hyperbolas extend the idea: constant sum or difference of distances to two foci.
- Motion described by a parameter · See it applied
The path of an object with constant horizontal speed and constant vertical acceleration is a parabola written with a parameter.
Related skills
- The incircle and the circumcircle · Related idea
The circumcenter is the locus of points equally far from the three vertices, as a parabola is the locus of points equally far from a focus and a line.
- Shifts, stretches, and reflections of graphs · Related idea
A parabola with its focus and directrix moved is the same locus, shifted, which the transformations of y = x squared describe.
- Equations of circles · Shared foundations
- Perimeter and area from coordinates · Shared foundations
- Proofs that use coordinates · Shared foundations
Open the interactive map to explore lessons and skill connections.