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:


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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.

FAQs (Frequently Asked Questions)

Question 1. What is the Difference Between Circle and Ellipse?

Answer: A circle is a closed curved shape that is flat. Instead of having all points the same distance from the centre point, though, an ellipse is shaped so that when you add together the distances from two points inside the ellipse (called the foci) they always add up to the same number.

Question 2. Do Ellipses have to Equal 1?

Answer: The ellipse is constructed out of tiny points of combinations of x's and y's. The equation always has to equal 1, which means that if one of these two variables is a 0, the other should be the same length as the radius, thus making the equation complete.

Question 3. What is A and B in an Ellipse?

Answer: (h, k) is the centre point, A is the distance from the centre to the end of the major axis, and B is the distance from the centre to the end of the minor axis. Remember that if the ellipse is horizontal, the larger number will go under the x. If it is vertical, the larger number will go under them.