Conic Sections - Hyperbolas Chapter 8, Section 3

About Hyperbolas Definition The set of all points in a plane such that the difference of the distances from two distinct points is a constant. Focus – one of the fixed points of the hyperbola Center – midpoint of the segment joining foci Vertex – turning point for the hyperbola

About Hyperbolas, continued… Transverse axis – segment joining the two vertices (also called the focal axis) Length is 2a Conjugate axis – segment perpendicular to the transverse axis through the center Length is 2b Asymptotes – lines the curve approaches as it recedes from the center Is the distance from the center to a focus E=c/a – called the eccentricity of the hyperbola

Horizontal Hyperbolas Center: (h,k) Focus: (h+c,k) (h-c,k) Transverse axis: y=k vertices: (h+a,k) (h-a,k) Asymptote:

Vertical Hyperbolas Center: (h,k) Focus: (h,k+c) (h,k-c) Transverse axis: x=h vertices: (h,k+a) (h,k-a) Asymptotes:

Examples – find the center, foci, vertices, asymptotes, transverse axis

Examples – write the equation in standard form

Classwork/Exit Slip Find the center, foci, vertices, asymptotes, transverse axis Write the equation of the hyperbola in standard form: Transverse axis length = 6, foci are (5,2) (-5,2) Center is (-3,1), focus is (2,1), e=5/4

Homework Page 663 Problems 1, 9, 47, 49 find the vertices, foci, asymptotes, transverse axis Problems 23, 28 write the equation in standard form