1) An ellipse can be obtained by compressing the coordinates of a circle along one axis. If the circle equation is x^2 + y^2 = 1, compressing the y-coordinates by a factor of b/a where b < a yields the ellipse equation (x/a)^2 + (y/b)^2 = 1. 2) The major axis of the ellipse is 2a and the minor axis is 2b. No part of the ellipse lies beyond x = ±a or y = ±b. 3) An ellipse can also be viewed as a circle stretched along one axis, so any ellipse equation can be obtained from a circle by stretching or compressing the coordinates.