[Maths Class Notes] on Ellipse Formula Pdf for Exam

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:

uploaded soon)

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.

2. Perimeter of Ellipse Formula

Perimeter of Ellipse Formula = [2pi 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.

3. 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.

4. 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

5. 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.