what is it?. definition: a hyperbola is the set of points p(x,y) in a plane such that the absolute...
DESCRIPTION
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) 9.5 HyperbolasTRANSCRIPT
What is it?
2 2
2 2
2 2
2 2
2 2
1. 4 16
2. ( 2) ( 1) 9
3. 16( 3) 9( 1) 225
4. 4 18
5. 2 4 8 81 0
x y
x y
x y
x y y
x x y y
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.
9.5 Hyperbolas9.5 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)
by xa
ay xb
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
9.5 Hyperbolas
1st
Either shorter
2a
2b
2 2
2 2 1 x y ORa b
2 2
2 2 1x h y ka b
2 2
2 2 1 y x ORa b
2 2
2 2 1y k x ha b
a2 alway
s comes
1st!
What is the equation?What is the equation?
2 2 1x y
What is the equation?What is the equation?
2 2
2 2
1
1
x y
x y
What is the equation?What is the equation?
22 1
4yx
What is the equation?What is the equation?
22
22
14
14
yx
yx
What is the equation?What is the equation?
22 1
9x y
What is the equation?What is the equation?2
2
22
19
19
x y
x y
How would you graph each?How would you graph each?
2 2 1x y
22 1
9x y
22 1
4yx
What is the equation?What is the equation?
22 1
16x y
What is the equation?What is the equation?2
2
22
116
116
x y
xy
What is the equation?What is the equation?
2 2
116 4x y
What is the equation?What is the equation?2 2
2 2
116 4
14 16
x y
y x
What is the equation?What is the equation?
22 1
25x y
What is the equation?What is the equation?2
2
22
125
125
x y
xy
2 2 1x y
22 1
9x y
22 1
4yx
22 1
16xy
2 2
14 16y x
22 1
25xy
Place the equation with the graph.
Example 1:Write the standard equation of the hyperbola with vertices (-5,0) and (5,0) and co-vertices (0, -2) and (0, 2). Sketch the graph.
Example 2: Write the standard equation of the hyperbola with V (0,-3) (0, 3) and CV(-6, 0) (6, 0)
Example 3:Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola.
2 2
116 4y x
Example 4:
Graph . Identify the center, vertices, foci, and asymptotes of the hyperbola.
136
22
xy
Example 5:
Graph 25y2 – 4x2 = 100. Identify the center, vertices, foci, and asymptotes of the hyperbola.
Assignment:Assignment:
