Math Wiki

Standard form of parabola

A parabola is the locus of a point which moves in a plane such that its distance from a fixed point (i.e. focus) is always equal to its distance from a fixed straight line (directrix). A parabola is a graph of a quadratic function, such as .

Standard Parabola

The general form of standard parabola is:  , where is a constant.

Important terms

  • The straight line passing through the focus and perpendicular to the directrix is called the Axis of the Parabola. The parabola is a symmetrical about its axis (i.e. line). It means if lies on parabola. then also lies on other sides of the axis.
  • The point which bisects every chord of the conic passing through it is called the Centre of the parabola.
  • The points of intersection of the conic section and the axis called Vertex. Vertex is point i.e. the origin is the vertex of the parabola.
  • The fixed point is known as Focus (denoted by ).
  • The fixed line is known as Directrix.
  • A chord passing through the focus is known as focal chord.
  • The straight line through focus and perpendicular to directrix is known as Axis.
  • The focal chord which is perpendicular to the axis is known as Latus Rectum. Since it passes through the focus of parabola, the equation of latus rectum is .

Solving equation (1) and we get: .

Parametric Equations

From the equation of parabola, we can write where is a parameter. Then, and

The equation and are called parametric equations.

General Form of Parabola

Finding the equation of parabola when focus and line of directrix are give Assume that the focus is , line of directrix as and point as whose locus is parabola. As we know that for parabola, (since e of parabola is 1) </math>PS^2=PN^2</math>

After simpligying the above equation and then replacing by and by , we get the required equation to parabola. The simplified form of general equation of parabola would look like:

, Where g, f and c are real constants.

See also