It is the locus of points such that the sum of their distance from two distinct fixed points is a constant.
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That's the definition of an ellipse.
One definition is that it is the locus of a point such that the sum of its distances from two fixed points (the foci) is a constant. There are several equivalent forms in coordinate geometry. Once the ellipse has been centred on the orign (using translations), (x/a)2 + (y/b)2 = 1 or x2 + (ey)2 = c2
No.
Yes, they are.
ellipse is the shape of an egg