# Area of an Ellipse

__Ellipse__

An ellipse is a curved line such that the sum of the distance of any point in it from two fixed points is constant. In the figure and are the two fixed points. The fixed points are called **foci**. The point is the **center** of the ellipse. is the **major axis **and is the **minor axis**. and are the **semi-axes**.

__Area of an Ellipse__

The area of a circle is given by the formula , which may be written as . If a circle is flattened it will take the form of an ellipse and the semi-axes of such an ellipse (like and in the given figure) will be the lengthened and shortened radii.

If stands for and stands for , it can be proved that the area of the ellipse can be found by substituting and in the formula for the area of the circle, which then gives the following formula for the area of an ellipse:

Where is the semi-major axis or major axis.

is the semi-minor axis orminor axis.

__Example__:

Find the radius of a circle equal in area as that of an ellipse whose axes are cm and cm.

__Solution__:

Here ,

area of the ellipse