Analytic Geometry in Two and Three Dimensions

631 Analytic Geometry in Twoand Three Sections andRotation of Equations SystemCHAPTER8 The oval-shaped lawn behind the White House inWashington, is called the Ellipse. It has views of theWashington Monument, the Jefferson Memorial, theDepartment of Commerce, and the Old Post Office Ellipse is 616 ft long, 528 ft wide, and is in the shape ofa conic section. Its shape can be modeled using the methodsof this chapter. See page 1/13/06 6:49 AM Page 631 Chapter 8 OverviewAnalytic Geometry combines number and form. It is the marriage of algebra and geom-etry that grew from the works of Frenchmen Ren Descartes (1596 1650) and Pierrede Fermat (1601 1665). Their achievements allowed Geometry problems to be solvedalgebraically and algebra problems to be solved geometrically two major themes ofthis book. Analytic Geometry opened the door for Newton and Leibniz to develop Sections , we will learn that parabolas, ellipses, and hyperbolas are all conicsections and can all be expressed as second-degree equations.

A is the set of all points in a plane equidistant from a particular line (the directrix) and a particular point (the ) in the plane. (See Figure 8.3.)focus parabola The line passing through the focus and perpendicular to the directrix is the (focal) of the parabola. The axis is the line of symmetry for the parabola. The point where the

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