What is the parametric equation of an ellipse?

1 Answer
Apr 21, 2018

Here is one example...

Explanation:

You can have (nsin(t),mcos(t)) when n!=m, and n and m do not equal to 1.

This is essentially because:

=>x=nsin(t)

=>x^2=n^2sin^2(t)

=>x^2/n^2=sin^2(t)

=>y=mcos(t)

=>y^2/m^2=cos^2(t)

=>x^2/n^2+y^2/m^2=sin^2(t)+cos^2(t)

Using the fact that sin^2(x)+cos^2(x)=1...

=>x^2/n^2+y^2/m^2=1

This is essentially an ellipse!

Note that if you want a non-circle ellipse, you have to make sure that n!=m