Equation of a Parabola

Conic Sections: An Introduction

A conic section is a curve formed by the intersection of a cone with a plane. Depending on how the plane is oriented, the curve will be one of the conic sections — circle, ellipse, parabola, or hyperbola:

  • A circle is the set of all points that area equally distant from a fixed point C, the center of the circle.
  • An ellipse is the set of all point surrounding two foci, or focus points, such that the sum of the distances from any point to each focus remains constant. An ellipse canbe oriented vertically (shaped higher than wide) or horizontally (shaped wider than high).
  • A parabola is the set of points that are equqally distant from the focus point and the directrix, a fixed line. A parabola can be oriented vertically (opening up or down) or horizontally (opening left or right).
  • A hyperbola is the set of all points around two foci, or focus points, such that the difference of the distances from any point to each focus remains constant. A hyperbola can be oriented vertically (opening up and down) or horizontally (opening left and right).

Equation of a Parabola

A parabola is the set of points that are equally distant from the focus point and the directrix. This Tab Tutor program will help you learn about the equation of a parabola and how to use it to derive the focus, vertex, and orientation. A useful glossary also introduces you to other features like the latus rectum and the axis of symmetry.