LEARN THINGS THE EASY WAY

# What is a Parabola

By the end of this lesson, you will be able to

• define parabola.
• identify different parts of a parabola.
• interpret different parts of parabola.
• draw a parabola.

## Parabola

A parabola is a plane curve formed by the set of all points such that for every point on the curve is equidistant from both a fixed point and a fixed line.

Different parts of parabola

The fixed point is called focus and the fixed line is called directrix of the parabola.

## Directrix of Parabola

A directrix is a straight line such that for every point on the parabola is equidistant from both the straight line and the focus of that parabola.

## Focus of Parabola

A special point is called focus of a parabola if for each point on the parabola is equidistant from both the special point and the directrix of that parabola.

## Axis of Symmetry

Axis of symmetry of a parabola is a line passing through focus and perpendicular to directrix. Again, a line passing through focus and vertex of a parabola is called the axis of symmetry of that parabola.

## Vertex of Parabola

A point on the parabola is said to be vertex if it also lies on the axis of symmetry. Consequently, the point of intersection between the parabola and the axis of symmetry is called the vertex of the parabola. This is the point at which the parabola is curved most sharply.

## Latus Rectum of Parabola

The latus rectum of a parabola is a line segment passing through the focus whose endpoins are on the parabola and parallel to the directrix of the parabola. It is a special chord of the parabola passes through the focus. It is also a unique chord passing through the focus and bisected by the axis of symmetry of the parabola.

## Focal Length

The distance between focus and vertex is called the focal length of the parabola. The focal length is equal to the perpendicular distance from the vertex to the directrix of the parabola.

Different parts of parabola is shown in figure.