Ellipse Formula

In geometry, an ellipse is described as a curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. In the following figure, F1 and F2 are called the foci of the ellipse.

Foci of EllipseEllipse has two types of axis – Major Axis and Minor Axis. The longest chord of the ellipse is the major axis. The perpendicular chord to the major axis is the minor axis which bisects the major axis at the center.

Ellipse
Ellipse Formula

Ellipse Formula

\[\large Area\;of\;the\;Ellipse=\pi r_{1}r_{2}\]

\[\large Perimeter\;of\;the\;Ellipse=2\pi \sqrt{\frac{r_{1}^{2}+r_{2}^{2}}{2}}\]

Where,
r1 is the semi major axis of the ellipse.
r2 is the semi minor axis of the ellipse.

Solved Examples

Question 1: Find the area and perimeter of a 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
= π $\times$ 10 $\times$ 5 cm2
= 157 cm2
Perimeter of the ellipse
= 2π $\sqrt{\frac{r_{1}^{2}+r_{2}^{2}}{2}}$= 2π $\sqrt{\frac{10^{2}+5^{2}}{2}}$ cm= 2π $\sqrt{\frac{100+25}{2}}$ cm

= 2π $\sqrt{\frac{125}{2}}$ cm= 49.64 cm
More topics in Ellipse Formula
Volume of an Ellipsoid Formula

Practise This Question

Himanshu tries to calculate the force exerted by 2 spherical objects of radius 1m each, having charges 3C and 5C and travelling at 4m/s with respect to each other. At an instant when the separation between them is 10 m, Himanshu theoretically calculates the force exerted by the one on another.  He only applies Coulomb's law and let us assume that he manages to apply it correctly but gets his answer wrong. Possible explanations could be?