The parabola as a locus

Definition — Parabola

A parabola is the locus of the points of the plane that are equidistant from a fixed point $F$, called the focus, and from a fixed line $d$, called the directrix (with $F$ not belonging to $d$): $P \in \text{parabola} \iff d(P, F) = d(P, d).$

In Year Two we had studied the parabola as the graph of $y = ax^2 + bx + c$: it was an object born from algebra. Now we have a purely geometric definition of it, which justifies its properties.

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Topics: Geometric loci
Concepts: Directrix · Point-line distance · Focus · Locus · Parabola · Line
Skills: Analytical geometry