Conics Name:Test REVIEW Pre-Calculus Hour: - Grosse Pointe Public Schools

Conics Test REVIEW Pre-Calculus

Name:_______________________________________ Hour:_______

Find the center and the exact radius of the circle. Then graph the circle.

1. ( - 5)2 + ( + 3)2 = 9

2.

( + 3)2 + 2 = 25

9

Center:_________

Center:_________

Radius:_________

Radius:_________

Find the equation of the circle in standard form that satisfies the given conditions.

3. The circle has center (0, 0) and passes through (-3, 4).

4. The circle has center (-4, -3) and passes through (-1, -1).

5. The endpoints of the diameter of the circle are (2, 6) and (-8, 4).

6. The circle has center (4, -3) and and is tangent to the x-axis.

Graph the ellipse and identify the center, vertices, and foci.

7. 2 + 2 = 1

9 25

8. 42 + 92 = 36

Center:___________ Vert:__________ Foci:________

Center:___________ Vert:__________ Foci:________

9. 2 + 42 = 36

Center:___________ Vert:__________ Foci:________

11. (-1)2 + (+2)2 = 1

4

9

10. ( + 1)2 + (-3)2 = 1

4

Center:___________ Vert:__________ Foci:________ 12. 36( + 4)2 + ( + 3)2 = 36

Center:___________ Vert:__________ Foci:________

Center:___________ Vert:__________ Foci:________

Find the standard form of the equation of each ellipse.

13. Foci (0, ?3), vertices (0, ?5)

14. Major axis horizontal with length 12; length of minor axis 4; center: (-1, 3)

15. Foci (?5, 0), length of major axis 12 17.

16. Endpoints of major axis: (2, 2) & (8, 2) Endpoints of minor axis: (5, 3) & (5, 1)

18.

Graph the hyperbola and identify the center, vertices, slopes of asymptotes, and foci.

19. 2 - 2 = 1

9 16

20. 42 - 2 = 16

Center: ___________ Vertices:___________ Foci:__________ Asymptotes:________

21. 4( - 1)2 - 9( + 2)2 = 36

Center: ___________ Vertices:___________ Foci:__________ Asymptotes:________

22. (+1)2 - (-2)2 = 1

25

9

Center:____________ Vertices:___________ Foci:__________ Asymptotes:________

23. (+2)2 - (-3)2 = 1

25

16

Center: ____________ Vertices:___________ Foci:__________ Asymptotes:________

24. (-2)2 ? (+3)2 = 1

25

16

Center: ___________ Vertices:___________ Foci:__________ Asymptotes:________

Center: ___________ Vertices:___________ Foci:__________ Asymptotes:________

Find the standard form of the equation of each hyperbola.

25. Foci (0, ?4), vertices (0, ?2)

26. Vertices (?4, 0), Asymptotes: = ?3

27. Endpoints of transverse axis: (?6, 0) Asymptotes: = ?2

28. Foci (0, ?3), length of transverse axis 2

29.

30.

Graph the parabola and identify the vertex, directrix, and focus.

31. 2 = -12

32. 2 = 8

Vertex: _______ Dir: _______ Focus: ___________

Vertex: _______ Dir: ____________ Focus:_________

33. 6( + 1)2 + 12( - 3) = 0

Vertex: _______ Dir: ___________ Focus: ________

35. ( + 2)2 = -8( + 2)

34. 2 - 12( + 2) = 0

Vertex: _______ Dir: __________ Focus:________

36. ( - 1)2 = -8

Vertex: _______ Dir: _______ Focus: ___________

Vertex: _______ Dir: ____________ Focus:_________

Write an equation in standard form for the parabola satisfying the given conditions.

37. Focus: (9, 0); Directrix: = -9

38. Focus: (-10, 0); Directrix: = 10

39. Vertex: (5, -2); Focus (7, -2)

40. Focus: (2, 4); Directrix: = -4

41.

42.

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