1. hyperbola
Last Updated: March 11, 2008

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

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

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

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

6. 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)

7. 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)
8.1 = c 7
(-1, -2)

8. Graph the following Hyperbola
Asymptotes
(-1, 12) 7
(-1, 5)
(-5, 5) 4 4
(3, 5) 7
(-1, -2)

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

10. 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)

11. 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)
6.7 = c 6
(-2, -3)

12. Graph the following Hyperbola
Asymptotes
(-2, 9) 6
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)

13. Graph the following Hyperbola
Asymptotes
(-2, 9) 6
(-2, 3)
(-5, 3) 3 3
(1, 3) 6
(-2, -3)

14. 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)
(5, 3) 4
(-1, -1)

15. 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)

16. Graph the following Hyperbola
Asymptotes
(-1, 7) 4
(-1, 3) 6 6
(-7, 3)
(5, 3) 4
(-1, -1)

17. Graph the following Hyperbola
Asymptotes
(-1, 7) 4
(-1, 3) 6 6
(-7, 3)
(5, 3) 4
(-1, -1)

18. 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)

19. 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)

20. Graph the following Hyperbola
Asymptotes
(-2, 6) 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)

21. Graph the following Hyperbola
Asymptotes
(-2, 6) 2
(-2, 4) 3 3
(-5, 4)
(1, 4) 2
(-2, 2)