Final answer:
A parabola can be defined using an algebraic equation showing its shape on the coordinate plane, or geometrically as the set of points equidistant from a focus and a directrix.
Step-by-step explanation:
The algebraic definition of a parabola involves a specific equation of the form y = ax^2 + bx + c, where 'a', 'b', and 'c' are constants that determine the parabola's shape and position on the coordinate plane. The variable 'x' represents the horizontal axis, while 'y' corresponds to the vertical axis; this equation describes the set of points (x, y) that form the parabola when plotted. In contrast, the geometric definition of a parabola describes it as the locus of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix). This definition emphasizes the distance relationship between the points on the parabola, the focus, and the directrix, providing a visual and conceptual understanding of the curve.