What is an Ellipse?
An ellipse is a geometric shape that resembles a stretched or elongated circle. It is defined as the set of all points in a plane such that the sum of the distances from two fixed points (called the foci) to each point on the ellipse remains constant.
The shape of an ellipse is determined by two parameters: the lengths of its major and minor axes. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter, perpendicular to the major axis and passing through the center of the ellipse.
Equation of Ellipse
The standard form of the equation for an ellipse centered at the origin (0,0) with major axis along the x-axis and minor axis along the y-axis is:
[Tex]\bold{\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1}[/Tex]
Where a is the length of the semi-major axis (half the length of the major axis) and b is the length of the semi-minor axis (half the length of the minor axis).
If the ellipse is centered at a point (h, k), the equation becomes:
[Tex]\bold{\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1}[/Tex]
Examples of Ellipse in Real-Life
Ellipse is a geometric shape that resembles a stretched circle. It is not only a fundamental concept in mathematics but also a very common to found throughout the natural world. From the orbits of celestial objects to fruits like watermelon or grapes, these are examples of ellipses in real life. In this article, we will discuss more such examples in detail.