1. 5.4 Hyperbolas
(part 1)
Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F1 and F2, called the foci, is a constant.
Doted lines are not part of the graph

2. (Just the Slope, a = Vertices, b = Co-Vertices)
5.4 Hyperbolas
Transverse axis
Conjugate Axis
Vertices
Co-vertices
Center
Foci
Asymptotes
(2a) length of V1 to V2
(2b) length of CV1 to CV2
Endpoints of TA
Endpoints of CA
Intersection of the 2 axes
Lie on inside of hyperbola & on TA
Horizontal Vertical
(Just the Slope, a = Vertices, b = Co-Vertices)

3. 5.4 Hyperbolas
Notes:
a2 is always the denominator of the ________ term when the equation is written in standard form.
_________ axis can be longer or ____________
The length of the transverse axis is _________
The length of the conjugate axis is _________
a2 + b2 = c2
1st
Either
shorter 2a 2b

5. Example 1:
Write the standard equation of the hyperbola with vertices (-4,0) and (4,0) and co-vertices (0, -3) and (0, 3). Sketch the graph.

6. Example 2:
Write the standard equation of the hyperbola with V(-7, 0) (7, 0) and CV (0,-4) (0, 4).

7. Homework
Worksheet
5.4