Circle: anyone knows how we get at A !=B Ellipse?

[Ryan$]

Hey guys what's up?
the teacher in my high school wrote this equation A*cosx + B*sinX and he said :
if A != B (not equal) as we get Ellipse
if A=B then we get circle

anyone knows how we get at A !=B Ellipse? how can I imagine that? I mean if A !=B how implicitly I can think over it?! thanks alot

 

[lev888]

Let's consider something simple: a rectangle with side lengths A, A, B, B. What happens when A = B? We get a square, a special kind of rectangle. Same thing with ellipses - when A = B we get a special ellipse, called a circle.