Vault Of Euclid

Equation of a Parabola from Focus and Directrix

Parametric equations and vector functions warmup

A parabola with focus \((2, -5)\) and directrix \(x = 6\)

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What you need first

The geometric definition of a parabola
The distance formula between two points
The distance from a point to a vertical line
Expanding binomial squares

What this problem tests

Tests the student's ability to translate the geometric definition of a parabola into an algebraic equation using the distance formula.

This is a standard analytic geometry problem often found in precalculus or early calculus courses when reviewing conic sections.

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