Dilation property of ellipses

An ellipse is the image of a circle under a dilation of the plane.

That is, it's a stretching or shrinking of a circle in one direction, relative to the center of the circle.

An ellipse can also be thought of as the image of a particular circle, such as one of radius 1, under a product of two perpendicular dilations of the plane relative to the center of the circle.