Practice and Problem-Solving Exercises

A Practice

See Problems 1, 2, and 3.

Graph each equation. Identify the conic section and describe the graph and its lines of symmetry. Then find the domain and range.

7. 3 y 2 − x 2 = 25 3 y squared , minus . x squared , equals 25
8. 2 x 2 + y 2 = 36 2 x squared , plus , y squared , equals 36
9. x 2 + y 2 = 16 x squared , plus . y squared , equals 16
10. 3 y 2 − x 2 = 9 3 y squared , minus . x squared , equals 9
11. 4 x 2 + 25 y 2 = 100 4 x squared , plus 25 , y squared , equals 100
12. x 2 + y 2 = 49 x squared , plus . y squared , equals 49
13. x 2 − y 2 + 1 = 0 x squared , minus , y squared , plus 1 equals 0
14. x 2 − 2 y 2 = 4 x squared , minus , 2 y squared , equals 4
15. 6 x 2 + 6 y 2 = 600 6 x squared , plus 6 , y squared , equals 600
16. x 2 + y 2 − 4 = 0 x squared , plus , y squared , minus 4 equals 0
17. 6 x 2 + 24 y 2 − 96 = 0 6 x squared , plus 24 , y squared , minus 96 equals 0
18. 4 x 2 + 4 y 2 − 20 = 0 4 x squared , plus 4 , y squared , minus 20 equals 0
19. x 2 + 9 y 2 = 1 x squared , plus 9 , y squared , equals 1
20. 4 x 2 − 36 y 2 = 144 4 x squared , minus , 36 y squared , equals 144
21. 4 y 2 − 36 x 2 = 1 4 y squared , minus , 36 x squared , equals 1

See Problem 4.

Identify the conic section. Then give the center, intercepts, domain, and range of each graph.

See Problem 5.

Match each equation with a graph in Exercises 22–27.

28. x 2 − y 2 = 9 x squared , minus . y squared , equals 9
29. 4 x 2 + 9 y 2 = 36 4 x squared , plus 9 , y squared , equals 36
30. y 2 − x 2 = 4 y squared , minus , x squared , equals 4
31. x 2 + 4 y 2 = 64 x squared , plus 4 , y squared , equals 64
32. 25 x 2 + 9 y 2 = 225 25 x squared , plus 9 , y squared , equals 225
33. y 2 − x 2 = 9 y squared , minus . x squared , equals 9

B Apply

Graph each equation. Describe the graph and its lines of symmetry. Then find the domain and range.

34. 9 x 2 − y 2 = 144 9 x squared , minus , y squared , equals 144
35. 11 x 2 + 11 y 2 = 44 11 x squared , plus 11 , y squared , equals 44
36. − 8 x 2 + 32 y 2 − 128 = 0 negative 8 x squared . plus , 32 y squared , minus 128 equals 0
37. 25 x 2 + 16 y 2 − 320 = 0 25 x squared , plus 16 , y squared , minus 320 equals 0

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