Parabola


This cheat sheet covers the high school math concept – Parabola.

Parabola

This concept is one of the important ones under Coordinate Geometry. It generally follows after Circle.

A parabola is defined as the set of all points in a plane equidistant from a given line L (called the directrix) and a given point F (called the focus), which not on the line L.

A parabola can also be defined as a conic section. It is created from the intersection of a right circular cone and a plane parallel to another plane that is tangential to the cone.

The parabola was studied by Menaechmus in an attempt to solve the problem of doubling a cube. The name ‘parabola’, which means ‘application’, was given by Apollonius who discovered many. Pascal considered the parabola as a projection of a circle, and Galileo showed that projectiles falling under uniform gravity follow parabolic paths.  Parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes and radar receivers.

A good knowledge of the basic formulae of coordinate geometry and straight line is a must to understand and solve problems related to parabola. Cheat sheets on Coordinate Geometry Basics and Straight Line are also available on this website.

This one page PDF covers summarised theory and the most important formulas related to the concept. Keep it handy while you’re revising the concept, especially before an exam.

The topics included in this cheat sheet are:

  • Standard equation
  • Equations with axes parallel to the coordinate axes
  • Equations with known focus and directrix
  • Parametric equation
  • Position of a point with respect to a parabola
  • Equation of tangents: Slope Form, Point Form and Parametric Form
  • Point of intersection of tangents
  • Pair of tangents from an external point
  • Equation of a normal: Slope Form, Point Form and Parametric Form
  • Point of intersection of normals
  • Three normals from a point
  • Equation of a chord with known end points
  • Equations of a chord with known mid point
  • Equation of chord of contact
  • Some relations related to parametric equations
  • Some properties of the parabola

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