1. Conic Sections - Hyperbolas
Chapter 8, Section 3

2. 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

3. 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

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

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

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

7. Examples – write the equation in standard form

8. 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

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