Engineering Calculus Notes 149

Engineering Calculus Notes 149 - 2.2 Parametrized Curves...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
2.2. PARAMETRIZED CURVES 137 B C F A E G D Figure 2.13: Trisecting an Angle 8. Show that the sum of the distances from a point on an ellipse to its two foci equals the major axis. (You may assume the equation is in standard form.) This is sometimes called the Gardener’s characterization of an ellipse: explain how one can construct an ellipse using a piece of string. 9. Show that the (absolute value of the) di±erence between the distances from a point on a hyperbola to its two foci equals the transverse axis. (You may assume the equation is in standard form.) 10. Show that the locus of the equation xy = 1 is a hyperbola. ( Hint: consider a di±erent coordinate system, using the diagonal and anti-diagonal as axes.)
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.2 Parametrized Curves Parametrized Curves in the Plane There are two distinct ways of specifying a curve in the plane. In classical geometric studies, a curve is given in a static way, either as the intersection of the plane with another surface (like the conical surface in Apollonius) or by a geometric condition (like xing the distance from a point or the focus-directrix property in Euclid and Pappus). This approach reached its modern version in the seventeenth century with Descartes and Fermats formulation of a curve as the locus of an equation in the coordinates of a...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online