# How are certain formulæ for areas of circles and ellipses related to calculus?

##### 2 Answers

Area of an Ellispe of the form

can be found by

which is an ellipse with

I hope that this was helpful.

Unlike the area, the perimeter of an ellipse cannot easily be written down in closed form, like the formula for the circumference of a circle.

#### Explanation:

There is a whole area of advanced maths dealing with elliptic integrals. Not only does this give the perimeter of an ellipse as an infinite series, but leads on to solutions for the period of a simple pendulum with large amplitude, [such as here].(http://www.rowan.edu/colleges/csm/departments/math/facultystaff/osler/125%20The%20Perimeter%20of%20an%20Ellipse%20as%20in%20Math%20Sci.pdf)