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11.1: Ellipses. Conics. The 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 Geometry.

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Conics
Conics

The 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 geometry
Analytic Geometry

The study of the geometric properties of objects using a coordinate system is called analytic geometry

(hence, the title of chapter 11).


Applications of ellipses
Applications of Ellipses

If an ellipse is rotated about the major axis, you obtain a football.


Applications of ellipses1
Applications of Ellipses

The path of planets in orbit is elliptical in shape.


Definition of the ellipse
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)