1. What is it?

2. 9.5 Hyperbolas
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.

3. 9.5 Hyperbolas Transverse axis Conjugate Axis Vertices Co-vertices
Center
Foci
Asymptotes
(2a) length of V to V
(2b) length of CV to CV
Endpoints of TA
Endpoints of CA
Intersection of the 2 axes
Lie on inside of hyperbola
Horizontal Vertical
(When centered at the origin)

4. 9.5 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. a2 always comes 1st!

6. 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.

7. Example 2:
Write the standard equation of the hyperbola with V (0,-4) (0, 4) and CV(-7, 0) (7, 0) V:
CV:
Foci: a= b= c=
Center:

8. Example 5:
Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola. V:
CV:
Foci: a= b= c=
Center: