Definition of a parabola

The parabola is the first curve we study systematically. It arises from a very simple geometric condition, involving a point and a straight line.

Definition — The parabola

The parabola is the locus of points equidistant from a fixed point (the focus) and a straight line (the directrix). Its equation in canonical form is $y=ax^2+bx+c.$

The coefficient $a$ cannot be zero: if $a=0$ the equation becomes that of a straight line. It is precisely the sign and value of $a$ that govern the opening and the direction of the curve.

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Topics: Parabola
Concepts: Directrix · Focus · Parabola
Functions: Parabola