Ellipse Formulas

Ellipse Formulas definition

The shape ellipse is connected with various formulas. The perimeter, area, equation, and other key characteristics can all be calculated using these elliptical formulas.

Formulas for the Ellipse's Perimeter

The perimeter of an ellipse is the whole length of its boundary and is measured in cm, m, ft, yd, and other units. The perimeter of an ellipse can be approximated using the following general formulas:

P ≈ π (a + b)

P ≈ π √[ 2 (a² + b²) ]

P ≈ π [ (3/2)(a+b) - √(ab) ]

where,

a is the length of the semi-major axis and b is the semi-minor axis length

Area of Ellipse Formula

The area of an ellipse is defined as the whole area or region covered by the elliptical in two dimensions, and it is measured in square units such as in², cm², m², yd², ft², and so on. Given the lengths of the main and minor axes, the area of an ellipse can be determined using a general formula. The formula for the ellipse area is as follows:

Area of ellipse = π a b

where a is the length of the semi-major axis and b is the length of the semi-minor axis. More Maths Formulas on the parent's page.

The eccentricity of an Ellipse Formula

The ratio of the distance of focus from the centre of the ellipse to the distance of one end of the ellipse from the centre of the ellipse is the eccentricity of an ellipse.

Eccentricity of an ellipse formula, e = c/a=√1−b²/a²

Latus Rectum of Ellipse Formula

The line drawn perpendicular to the transverse axis of an ellipse and passing through the foci of the ellipse is known as the latus rectum. The formula for calculating the length of an ellipse's latus rectum is as follows:

L = 2b²/a

The formula for Equation of an Ellipse

The ellipse formula equation aids in the representation of an ellipse in algebraic form. The equation of an ellipse can be found using the following formula:

Ellipse equation with centre at (0,0) : x²/a² + y²/b² = 1

Ellipse equation with centre at (h,k) : (x-h)² /a² + (y-k)²/ b² =1

Properties of an Ellipse

Several characteristics distinguish an ellipse from other comparable shapes. These are the properties of an ellipse:

An ellipse is created by a plane intersecting a cone at the angle of its base.
All ellipses have two foci or focal points. The sum of the distances from any point on the ellipse to the two focal points is a constant value.
There is a centre and a major and minor axis in all ellipses.
The eccentricity value of all ellipses is less than one.

Ellipse Formulas