What is an Ellipse?

Ellipse is a shape that’s very common in our day-to-day life. If you’re an athlete, you will observe that the running track is in the shape of an ellipse. Similarly, an egg is also in the shape of an ellipse. In geometry, an ellipse is a shape that has similar properties to a circle but is a flattened circle. In simpler words, it’s an oval. 

What is Parabola?

Before we dive deep into the basics of ellipses, let’s understand what a conic section is. There are three types of conic sections which include:

  • Ellipse
  • Parabola
  • Hyperbolas

In geometry, a  parabola is a curve. Here, a point on the parabola is at a fixed point and a fixed straight line. For example, while playing football when you kick the ball, it arcs up into the air and comes down again forming a parabola. Another example of a parabola can be witnessed in the “M” of McDonald’s. The curves present in the letter “M” is an example of a parabola. 

On the other hand, a hyperbola is a curve between two fixed points that remain constant. For example, the grip lines in the basketball are in the form of hyperbolas as they run between two fixed points. 

Now, in this article, we will be understanding the basic concepts of ellipses in detail. 

Basics of Ellipses

Let us understand the basic concepts related to ellipses in detail. 

1. Focus: There are two focus points on an ellipse. The plural form of focus is foci. The focus points always lie on the longest axis.

2. Center: When a line joins two focus points, the midpoint on that line is called the center. 

3., Major Axis and Minor Axis: Major axis is the largest width across the ellipse, whereas, the minor axis is the shortest width across the ellipse. 

4. Transverse Axis and Conjugate Axis: When a line crosses the center of the ellipse and two focus points, it’s called the transverse axis. Similarly, when a line passes through the midpoint of the ellipse and at the same time is perpendicular to the transverse axis, it is called the conjugate axis.

5. Latus Rectum: A line segment that’s drawn perpendicular to the transverse axis and passes through the two focus points, it’s called the latus rectum. 

6. Eccentricity: The eccentricity defines how off the ellipse is from its midpoint. The eccentricity of an ellipse is always strictly below 1. 

Formulas of Ellipse

Ellipses have different formulas. These formulas include area, perimeter, eccentricity, and much more. The basic formulas of area and perimeter are explained below: 

1. The area of an ellipse. In simple words, the area is the measurement of the amount of region covered by the ellipse. It can be calculated with the help of the formula:

Area of Ellipse = πab

where, 

a = length of semi-major axis

b = length of semi-minor axis

The area of an ellipse can be expressed in square units of inches, centimeters, meters, yards, feet, and much more. 

2. The perimeter of an ellipse. In simple words, the perimeter is the measurement of the length of the boundaries of the ellipse. It can be calculated with the help of the formula: 

The perimeter of the Ellipse ≈ π (a + b)

where,


a = length of semi-major axis

b = length of semi-minor axis

The above formula can be used when the values of “a” and “b” are approximately equal. The perimeter of an ellipse can be expressed in inches, centimeters, meters, yards, feet, and much more. 

Ellipses, Parabolas, and Hyperbolas are conic structures that can be witnessed very frequently in our day-to-day lives. Cuemath is revolutionizing the way students learn math. To learn more about ellipses in detail, inclusive of their properties, operations, and much more, visit Cuemath!

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