Hyperbolas

1
Hyperbolas

• Date ______________

2
Hyperbolas with Center (0,0)
9.5 Hyperbolas
Horizontaltransverse axis
V1(a, 0)
V2(a, 0)
asymptotes
3
9.5 Hyperbolas
y
Verticaltransverse axis
V2(0, b)
x
asymptotes
V1(0, b)
4
Hyperbolas with Center (h,k)
y
V1
y
(h,k)
(h,k)
V1
V2
x
x
V2
5
Graph the hyperbola and find the vertices.
a2 36
b2 64
a 6
b 8
vertices (-6,0) (6, 0)
6
Graph the hyperbola and find the vertices.
a2 64
b2 100
a 8
b 10
vertices (0, 10) (0,-10)
7
Graph the hyperbola and find the vertices.
center (2, 1)
a2 9
b2 16
a 3
b 4
vertices (-1, -1) (5,-1)
8
Graph the hyperbola and find the vertices.
center (-2, 2)
a2 9
b2 16
a 3
b 4
vertices (-2,6) (-2,-2)
9
Write the equation for the hyperbola in standard
form. Graph.
-2x2 y2 4x 6y 3 0
y2 6y - 2x2 4x -3
9
1
y2 6y ___- 2(x2 2x ___) -3
9
- 2
(y 3)2- 2(x 1)2 4
4
10
center (1, 3)
b2 4
a2 2
b 2
a 1.4
vertices (1,-1) (1, -5)
11
Write the equation for the hyperbola in standard
form. Graph.
4x2 - 25y2 - 8x 100y - 196 0
4x2 8x - 25y2 100y 196
1
4
4(x2 2x ___) -25(y2 4y ___) 196
4
4(x 1)2 - 25(y 2)2 100
- 100
100
12
center (1, 2)
b2 4
a2 25
b 2
a 5
vertices (6,2) (-4, 2)
13
Write the equation for the hyperbola in standard
form. Graph.
x2 y2 6x 10y 20 0
x2 6x y2 10y 20
9
25
x2 6x ___ (y2 10y ___) 20
9
- 25
(x 3)2 (y 5)2 4
4
14
center (3, -5)
b2 4
a2 4
b 2
a 2
vertices (1,-5) (5,-5)
15
Finding the foci.
a2 b2 c2
F1(c, 0)
F2 (c, 0)
16
Finding the foci.
F1(0,c)
a2 b2 c2
F2 (0,-c)
17
Find the foci.
36 64 c2 100 c2 10 c
(-10,0)
(10,0)