What is the parametric equation of an ellipse?

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Answer 1 · 2018-04-21T00:39:33

Here is one example...

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#