What is a parabola?
Answer
A parabola is the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix.
The working
Definition
Every point on a parabola is the same distance from the focus as from the directrix. This ratio of distances, the eccentricity, equals 1.
Standard equation
A parabola opening rightward has the equation y² = 4ax, where a is the distance from the vertex to the focus.
Key features
The vertex is the turning point, the axis is the line of symmetry through the focus, and the latus rectum has length 4a.
As a conic
A parabola is formed when a plane cuts a cone parallel to its slant side. It is one of the conic sections.
Example
The graph of y = x² is a parabola opening upward with its vertex at the origin.
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