# Ellipse Formula

## What is an Ellipse?

An ellipse is a set of all the points on a plane surface whose distance from two fixed points G and F add up to a constant.

An ellipse mostly looks like a squashed circle:

In this article, we are going to discuss the perimeter of the ellipse formula, the circumference of the ellipse formula, the ellipse volume formula, area of the ellipse formula.

### What are the Properties of Ellipse?

• Ellipse has two focal points, also called foci.

• The fixed distance is called a directrix.

• The eccentricity of the ellipse lies between 0 to 1. 0 ≤ e < 1.

• The total sum of each distance from the locus of an ellipse to the two focal points is constant.

• Ellipse has one major axis and one minor axis and a center.

### Ellipse Formula

1. Area of Ellipse Formula

Area of the Ellipse Formula = πr1r2

Where,

r1 is the semi-major axis of the ellipse.

r2 is the semi-minor axis of the ellipse.

1. Perimeter of Ellipse Formula

Perimeter of Ellipse Formula = $2\pi \sqrt{\frac{r_{1}^{2} + r_{2}^{2}}{2}}$

Where,

r1 is the semi-major axis of the ellipse.

r2 is the semi-minor axis of the ellipse.

1. Ellipse Volume Formula

We can calculate the volume of an elliptical sphere with a simple and elegant ellipsoid equation:

Ellipse Volume Formula = 4/3 * π * A * B * C, where: A, B, and C are the lengths of all three semi-axes of the ellipsoid and the value of π = 3.14.

1. General Equation of an Ellipse

When the centre of the ellipse is at the origin (0, 0) and the foci are on the x-axis and y-axis, then we can easily derive the ellipse equation.

The equation of the ellipse is given by;

x2/a2 + y2/b2 = 1

1. Circumference of Ellipse Formula

π(a + b)

Where,

r1 is the semi-major axis of the ellipse.

r2 is the semi-minor axis of the ellipse.

### Solved Examples

Question 1. Find the area of an ellipse whose semi-major axis is 10 cm and semi-minor axis is 5 cm.

Solution:

Given,

Semi major axis of the ellipse = r1 = 10 cm

Semi minor axis of the ellipse = r2 = 5 cm

Area of the ellipse

= πr1r2

= 3.14 × 10 × 5 cm2

= 157 cm2

### Key Points

• An ellipse and a circle are both examples of conic sections.

• A circle is a special case of an ellipse, with the same radius for all points.

• By stretching a circle in the x or y direction, an ellipse is created.