11.4. Hyperbola - Asymptotes Other Points 7(y – 3 2 –(x...

11.4: The Hyperbola
Equations, given center (h, k), a = distance from center to vertex, c = distance from
center to either focus, b
2
= c
2
– a
2
, and transverse axis equal or parallel to:
( 29 ( 29
( 29 ( 29
2 2
2 2
2 2
2 2
[1] : 1, :
[2] : 1, :
x h y k
b
x axis oblique asymptote y x
a b a
y k x h
a
y axis oblique asymptote y x
a b b
- -
- - = = ±
- -
- - = = ±
Find an equation for the hyperbola described.  Graph each equation.
1.  (h, k) = (0, 0); F
1
= (0, 5); V
1
= (0, 3) 2.  V
1,2
= ( ± 4, 0); Asymptote: y = 2x
Write an equation for each hyperbola:
3. y = ± 3x 4. y =
1
/
3
x

Find and discuss the equation and graph the following hyperbolas with foci & asymptotes:
5. y
2
– 4x
2
= 16 6.  Center: (1, 4); focus: (-2, 4); V
1
= (0, 4)
Equation
Center
Transverse Axis
a, b, c
Vertices
Foci
Asymptotes