1. hyperbola
Last Updated: October 11, 2005
Jeff Bivin -- LZHS

2. Hyperbola
The set of all co-planar points whose difference of the distances from two fixed points (foci) are constant.
foci
foci
Jeff Bivin -- LZHS

3. Co-vertices endpoints of conjugate axis
Hyperbola
Center: (h, k)
conjugate axis
vertex
vertex
transverse axis
Co-vertices endpoints of conjugate axis
Jeff Bivin -- LZHS

4. Co-vertices endpoints of conjugate axis
Hyperbola
vertex
transverse axis
Co-vertices endpoints of conjugate axis
conjugate axis
vertex
Jeff Bivin -- LZHS

5. Hyperbola c2 = a2 + b2 Distance from center to vertex = a
Distance from center to co-vertex = b
Distance from center to foci = c b a
c2 = a2 + b2 c
Length of transverse axis = 2a
Length of conjugate axis = 2b

6. Hyperbola
The Latus Rectum (LR) is a chord passing through the focus that is perpendicular to an extended transverse axis.
The length
of the L.R. is
Distance from center to vertex = a
Distance from center to co-vertex = b
Distance from center to foci = c
Jeff Bivin -- LZHS

7. Graph the following Hyperbola
Center: (-1, 5)
a = 4 in x direction
b = 7 in y direction
(-1, 12) 7
(-1, 5)
(-5, 5) 4 4
(3, 5) 7
(-1, -2)
Jeff Bivin -- LZHS

8. Graph the following Hyperbola
Center: (-1, 5)
a = b = 7
a2 + b2 = c2
(-1, 12)
= c2
= c2
65 = c2 7
foci
(-1, 5)
(-5, 5) 4 4
(3, 5) 7
(-1, -2)
Jeff Bivin -- LZHS

9. Graph the following Hyperbola
Asymptotes
(-1, 12) 7
(-1, 5)
(-5, 5) 4 4
(3, 5) 7
(-1, -2)
Jeff Bivin -- LZHS

10. Graph the following Hyperbola
Asymptotes
(-1, 12) 7
(-1, 5)
(-5, 5) 4 4
(3, 5) 7
(-1, -2)
Jeff Bivin -- LZHS

11. Graph the following Hyperbola
Find the Length of the LR.
a = 4 b = 7 c =
(-1, 12) 7
(-1, 5)
(-5, 5) 4 4
(3, 5) 7
(-1, -2)
Jeff Bivin -- LZHS

12. Graph the following Hyperbola
Center: (-1, 5)
Vertices: (-5, 5) (3, 5)
Co-Vertices: (-1, 12) (-1, -2)
Foci:
(-1, 12)
Length of Transverse axis: 8
Length of Conjugate axis: 14 7
(-1, 5)
Asymptotes
(-5, 5) 4 4
(3, 5) 7
(-1, -2)
Jeff Bivin -- LZHS

13. Graph the following Hyperbola
Center: (-2, 3)
a = 6 in y direction
b = 3 in x direction
(-2, 9) 6
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)
Jeff Bivin -- LZHS

14. Graph the following Hyperbola
Center: (-2, 3)
a = b = 3
a2 + b2 = c2
(-2, 9)
= c2
= c2
45 = c2 6
foci
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)
Jeff Bivin -- LZHS

15. Graph the following Hyperbola
Asymptotes
(-2, 9) 6
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)
Jeff Bivin -- LZHS

16. Graph the following Hyperbola
Asymptotes
(-2, 9) 6
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)
Jeff Bivin -- LZHS

17. Graph the following Hyperbola
Find the Length of the LR.
a = 6 b = 3 c =
(-2, 9) 6
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)
Jeff Bivin -- LZHS

18. Graph the following Hyperbola
Center: (-2, 3)
Vertices: (-1, 3) (-5, 3)
Co-Vertices: (-2, -3) (-2, 9)
Foci:
(-2, 9)
Length of Transverse axis: 12 6
Length of Conjugate axis: 6
(-2, 3)
Asymptotes
(-5, 3) 3 3
(1, 3) 6
(-2, -3)
Jeff Bivin -- LZHS

19. Graph the following Hyperbola
4x2 + 8x - 9y2 + 54y - 53 = 168
(4x2 + 8x ) - (9y2 - 54y ) =
4(x2 + 2x + 12) - 9(y2 - 6y + 32) =
4(x + 1)2 - 9(y - 3)2 = 144
144 36 16
Jeff Bivin -- LZHS

20. Graph the following Hyperbola
Center: (-1, 3)
a = 6 in x direction
(-1, 7)
b = 4 in y direction 4
(-1, 3) 6 6
(-7, 3)
(3, 5) 4
(-1, -1)
Jeff Bivin -- LZHS

21. Graph the following Hyperbola
Center: (-1, 3)
a = b = 4
foci
a2 + b2 = c2
(-1, 7)
= c2
= c2 4
52 = c2
(-1, 3) 6 6
(-7, 3)
(5, 3) 4
(-1, -1)
Jeff Bivin -- LZHS

22. Graph the following Hyperbola
Asymptotes
(-1, 7) 4
(-1, 3) 6 6
(-7, 3)
(5, 3) 4
(-1, -1)
Jeff Bivin -- LZHS

23. Graph the following Hyperbola
Asymptotes
(-1, 7) 4
(-1, 3) 6 6
(-7, 3)
(5, 3) 4
(-1, -1)
Jeff Bivin -- LZHS

24. Graph the following Hyperbola
Find the Length of the LR.
a = 6 b = 4 c =
(-1, 7) 4
(-1, 3) 6 6
(-7, 3)
(5, 3) 4
(-1, -1)
Jeff Bivin -- LZHS

25. Graph the following Hyperbola
Center: (-1, 3)
Vertices: (-7, 3) (5, 3)
Co-Vertices: (-1, 7) (-1, -1)
Foci:
(-1, 7)
Length of Transverse axis: 12
Length of Conjugate axis: 8 4
(-1, 3)
Asymptotes: 6 6
(-7, 3)
(5, 3) 4
(-1, -1)
Jeff Bivin -- LZHS

26. Graph the following Hyperbola
4x2 + 16x - 9y2 + 72y - 5 = 87
4x2 + 16x y2 + 72y =
4(x2 + 4x + 22) - 9(y2 - 8y + (-4)2) =
4(x + 2)2 - 9(y - 4)2 = -36
-36 -9 4
Jeff Bivin -- LZHS

27. Graph the following Hyperbola
Center: (-2, 4)
a = 2 in y direction
b = 3 in x direction
(-2, 6) 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)
Jeff Bivin -- LZHS

28. Graph the following Hyperbola
Center: (-1, 3)
a = b = 3
a2 + b2 = c2
(-2, 6)
= c2
4 + 9 = c2
foci
13 = c2 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)
Jeff Bivin -- LZHS

29. Graph the following Hyperbola
Asymptotes
(-2, 6) 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)
Jeff Bivin -- LZHS

30. Graph the following Hyperbola
Asymptotes
(-2, 6) 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)
Jeff Bivin -- LZHS

31. Graph the following Hyperbola
Find the Length of the LR.
a = 2 b = 3 c =
(-2, 6) 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)
Jeff Bivin -- LZHS

32. Graph the following Hyperbola
Center: (-2, 4)
Vertices: (-2, 6) (-2, 2)
Co-Vertices: (-5, 4) (1, 4)
Foci:
(-2, 6)
Length of Transverse axis: 4
Length of Conjugate axis: 6 2
Asymptotes
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)
Jeff Bivin -- LZHS

33. That's
All
Folks