Parts of a Parabola

Some important terms and parts of a parabola are:

• Focus: Focus is the fixed point of a parabola.

• Directrix:  The directrix of a parabola is the line perpendicular to the axis of a parabola.

• Focal Chord: The chord that passes through the focus of a parabola, cutting the parabola at two distinct points, is called the focal chord.

• Focal Distance:  The focal distance is the distance of a point (x₁, y₁) on the parabola from the focus.

• Latus Rectum: A latus rectum is a focal chord that passes through the focus of a parabola and is perpendicular to the axis of the parabola. The length of the latus rectum is LL’ = 4a.

• Eccentricity: The ratio of the distance of a point from the focus to its distance from the directrix is called eccentricity (e). For a parabola, eccentricity is equal to 1, i.e., e = 1.

A parabola has four standard equations based on the orientation of the parabola and its axis. Each parabola has a different transverse axis and conjugated axis.

The following are the observations made from the standard form of equations of a parabola:

• A parabola is symmetrical w.r.t its axis. For example, y² = 4ax is symmetric w.r.t the x-axis, whereas x² = 4ay is symmetric with respect to the y-axis.

• If a parabola is symmetric about the x-axis, then the parabola opens towards the right if the x-coefficient is positive and towards the left if the x-coefficient is negative.

• If a parabola is symmetric about the y-axis, then the parabola opens upwards if the y-coefficient is positive and downwards if the y-coefficient is negative.

The following are the standard equations of a parabola when the axis of symmetry is either parallel to the x-axis or y-axis and the vertex is not at the origin. 

Standard form of a parabola is y = ax² + bx + c where a, b, and c are real numbers and a is not equal to zero. A parabola is defined as the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.

In this article, we will understand what is a Parabola, the standard equation of a Parabola, related examples and others in detail.