11.1: Ellipses

ConicsThe conics get their name from the fact that they can be

formed by passing a plane through a double-napped cone (two right circular cones placed together, nose-

to-nose).

Analytic GeometryThe study of the

geometric properties of objects using a

coordinate system is called analytic

geometry(hence, the title of

chapter 11).

Applications of EllipsesIf an ellipse is rotated about the major axis,

you obtain a football.

Applications of EllipsesThe path of planets in orbit is elliptical in shape.

Definition of the Ellipse• An ellipse is the set

of all points such that the sum of the distance from P to F1 and P to F2 is k.

• PF1 + PF2 = k

(F1 and F2 are the foci)