Does an ellipse have asymptotes

Answer 1

ellipses do have asymptotes, but they are imaginary, so they are generally not considered asymptotes.

If the equation of the ellipse is in the form

a(x-h)^2 + b(y-k)^2 = 1

then the asymptotes are the lines

a(y-k)+bi(x-h)=0

ai(y-k)+b(x-h)=0

the intersection of the asymptotes is the center of the ellipse.

Answer 2

No. The definition of an asymptote is a parabolic curve that when extended to infinity, meets a specific line such as x=2, y=0, etc. Since an ellipse does not extend infinitely and is a closed shape, it does not have asymptotes.