# 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.

Ellipse 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 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,

r_{1} is the semi major axis of the ellipse.

r_{2} 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 = r

Semi minor axis of the ellipse = r

Semi major axis of the ellipse = r

_{1 }= 10 cmSemi minor axis of the ellipse = r

_{2 }= 5 cmArea of the ellipse

= πr

= πr

_{1}r_{2 }= π $\times$ 10 $\times$ 5 cm^{2 }= 157 cm^{2}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

= 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

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