# Ellipse Shape

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

- define ellipse.
- identify different parts of an ellipse.
- interpret different parts of an ellipse.
- draw an ellipse.

## Ellipse

An ellipse is a plane closed curve formed by the set of all points surrounding two fixed points such that the sum of distances from two fixed points to every point on the curve is constant.

Different parts of ellipse

Each fixed point is called focus of the ellipse. The plural of focus is foci. The midpoint of line segment connected to two foci is the center of the ellipse.

## Center of Ellipse

The midpoint of line segment connected to two foci is the center of the ellipse. It is also the intersection of major axis and minor axis. The two axes bisect as well as are perpendicular to each other at the centre of an ellipse.

## Focus of Ellipse

In plane geometry, by definition, an ellipse is a locus of points such that the sum of distances from one of those points to two fixed points inside the ellipse is constant. Each of two fixed points is called the focus of the ellipse. The plural of focus is foci.

## Major Axis of Ellipse

A major axis is a line segment whose endpoints are on the boundary of the ellipse and passes through two foci. It is also the largest diameter of an ellipse.

### Length of Major Axis

The length of major axis is equal to the sum of distances from two focus points to any point on the boundary of the ellipse. The length of the major axis is equal to the length of the longest diameter of an ellipse.

If P is any ponit on the ellipse and; c and d are the distances from P to two foci,

the length of the major axis = c+d = 2a

where 2a is the length of the longest diameter.

## Minor Axis of Ellipse

A minor axis is a line segment whose endpoints are on the boundary of the ellipse and passes through centre and perpenducular to major axis.

### Length of Minor Axis

The length of minor axis is the shortestest diameter of an ellipse. It is generally denoted by 2b.

Different parts of ellipse is shown in figure

## Latus Rectum of Ellipse

A latus rectum is a line segment whose endpoints are on the boundary of the ellipse passing through a focal point and perpenducular to major axis.

### Semi-Latus Rectum

One half the latus rectum is the semi latus rectum.