The
locus of
points in the
plane with some common
sum-of-
distances to 2
points:
{ P : d(A,P) + d(B,P) = 2R }
for points A,B in the plane. A and B are known as the
foci (sing.
focus) of the ellipse.
To draw an ellipse, take a sheet of paper and stick 2 thumbtacks through A and B. Now tie a piece of string into a loop. Slip the loop around the 2 thumbtacks, and put a pen in it. Trace that pen around the tacks while holding the string taut. It's obvious the result has to be an ellipse.