Chapter 10 Conic Sections

Chapter Sections 10.1 – The Parabola and the Circle 10.2 – The Ellipse 10.3 – The Hyperbola 10.4 – Nonlinear Systems of Equations and Their Applications Chapter 1 Outline

§ 10.3 The Hyperbola

Graph Hyperbolas Hyperbola A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points, called the foci, is a constant. For every point on the hyperbola, the difference M – N is the same constant.

Graph Hyperbolas A hyperbola has two vertices. The vertices are the points where the graph crosses the x- or y-axes. The point halfway between two vertices is the center of the hyperbola. The line through the vertices is called the transverse axis.

Graph Hyperbolas

Graph Hyperbolas Hyperbola with Its Center at the Origin Transverse Axis Along x-Axis (Opens to the Right and Left) Transverse Axis Along y-Axis (Opens Upward and Downward) Asymptotes

Graph Hyperbolas Example Determine the equations of the asymptotes of the hyperbola with the equation and draw the hyperbola using the asymptotes. The value of a2 is 9; the positive square root of 9 is 3. The value of b2 is 16; the positive square root of 16 is 4. The asymptotes are: continued

Graph Hyperbolas