Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write an equation of a hyperbola with the given values, foci, or vertices. Assume that the transverse axis is horizontal.

8. a = 3 , b = 4 eh equals 3 comma b equals 4
9. a = 12 , c = 13 eh equals 12 comma c equals 13
10. b = 9 , c = 10 b equals 9 comma c equals 10
11. a = 7 , b = 11 eh equals 7 comma b equals 11
12. foci ( ± 13 , 0 ) , open plus minus 13 comma 0 close comma  vertices ( ± 12 , 0 ) open plus minus 12 comma 0 close
13. foci ( ± 3 , 0 ) , open plus minus 3 comma 0 close comma  vertices ( ± 2 , 0 ) open plus minus 2 comma 0 close

See Problem 2.

Find the vertices, foci, and asymptotes of each hyperbola. Then sketch the graph.

14. y 2 81 − x 2 16 = 1 fraction y squared , over 81 end fraction , minus , fraction x squared , over 16 end fraction , equals 1
15. y 2 49 − x 2 64 = 1 fraction y squared , over 49 end fraction , minus , fraction x squared , over 64 end fraction , equals 1
16. x 2 121 − y 2 144 = 1 fraction x squared , over 121 end fraction . minus . fraction y squared , over 144 end fraction . equals 1
17. x 2 64 − y 2 36 = 1 fraction x squared , over 64 end fraction , minus , fraction y squared , over 36 end fraction , equals 1
18. y 2 25 − x 2 100 = 1 fraction y squared , over 25 end fraction , minus . fraction x squared , over 100 end fraction . equals 1
19. 81 y 2 − 9 x 2 = 729 81 y squared , minus , 9 x squared , equals 729
20. 4 y 2 − 25 x 2 = 100 4 y squared , minus , 25 x squared , equals 100
21. 36 x 2 − 8 y 2 = 288 36 x squared , minus , 8 y squared , equals 288
22. 14 y 2 − 28 x 2 = 448 14 y squared , minus , 28 x squared , equals 448

23. Satellite Dish The diagram below models a satellite dish and the small reflector inside it. Suppose F 1 f sub 1  and F 2 f sub 2  are 7 meters apart, and F 1 f sub 1  is 1 meter from the vertex of the small reflector. What equation best models the small reflector?

    
    Image Long Description

See Problem 3.

B Apply

24. Think About a Plan The path that Voyager 2 made around Jupiter followed one branch of a hyperbola. Find an equation that models the path of Voyager 2 around Jupiter, given that a = 2,184,140  km eh equals . 2,184,140 . km  and c = 2,904,906.2  km. c equals . 2,904,906.2 . km.  Use the horizontal model.
    • What information do you need to write the equation?
    • How can you use the given information to find the information you need?

Write an equation of a hyperbola with the given foci and vertices.

25. foci ( ± 5 , 0 ) , open plus minus 5 comma 0 close comma  vertices ( ± 3 , 0 ) open plus minus 3 comma 0 close
26. foci ( 0 , ± 13 ) , open 0 comma plus minus 13 close comma  vertices ( 0 , ± 5 ) open 0 comma plus minus 5 close
27. foci ( 0 , ± 2 ) , open 0 comma plus minus 2 close comma  vertices ( 0 , ± 1 ) open 0 comma plus minus 1 close
28. foci ( ± 5 , 0 ) , open plus minus square root of 5 comma 0 close comma  vertices ( ± 2 , 0 ) open plus minus 2 comma 0 close

Table of Contents