Name:
Parabolas
Score: ____/24
____/6 Identify focus and directrix of the graph of each equation
1. –y + x2 = 3
2. –x – 3y2 = 0
3. 8x = y2 + 6y + 9
Focus:
Focus:
Focus:
Directrix:
Directrix:
Directrix:
___/6 Write an equation of a parabola with vertex at the origin.
4. Focus at (-2,0)
5. Directrix at x = 3
6. Focus at (0,-3)
7. Directrix at x = -2
8. Directrix at y = -3
9. Focus at (3,0)
____/12 Identify the vertex, focus and directrix of the graph of each equation. Then sketch a graph.
10. 𝑦 + 1 =
Vertex:
−1
(𝑥
4
11. X = 2y2
Vertex:
− 3)2
12. y2 – 4x – 2y = 3
Vertex:
Focus:
Focus:
Focus:
Directrix:
Directrix:
Directrix:
y
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Conics Packet
5
1
1
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5
y
y
1
Rev A
4
5
x
Name:
Circles
Score: ____/21
____/3 Write an equation of a circle with the given center and radius
13. center (-1, 0) radius 6
14. center (4,-4) radius 1.5
15. center (5, -1) radius 1.1
____/6 Find the center and radius of each circle.
16. (x+1)2 + (y-8)2= 1
17. x2 + (y+3)2= 9
18. x2 + y2= 144
Center:
Center:
Center:
Radius:
Radius:
Radius:
____/3 Write an equation for each translation.
19. x2 + y2= 9; right 4 down 2
20. x2 + y2= 12; left 2 up 5
21. x2 + y2= 36; left 8 down 6
____/9 Use the center and radius to graph each circle
22. x2 + (y+3)2 = 121
Center:
23. (x-8)2 + (y+9)2 = 64
Center:
Radius:
Radius:
Radius:
y
–5
–4
–3
–2
Conics Packet
24. (x+7)2 + (y+2)2 = 80
Center:
y
y
5
5
5
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1
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–1
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Rev A
4
5
x
Name:
Ellipse
Score: ____/18
____/6 Write an equation of each ellipse in standard form with center at origin and with the given
characteristics
25. Height 8, width 18
26. Foci(±5,0) co-vertices (0, ±2)
27. Height 3, width 1
28. vertex(6,0) co-vertex (0, -5)
29. vertex(0,2) co-vertex (-1, 0)
30. vertex(-2,0) co-vertex (0, -1)
____/12 Find the foci, vertices and co-vertices for each equation of an ellipse. Then graph the ellipse.
31.
𝑥2
36
+
𝑦2
81
32. 16x2 + 25y2 = 1600
=1
33.
Focus:
Focus:
𝑦2
144
=1
Vertices:
Co-Vertices:
Co-Vertices:
+
Focus:
Vertices:
Vertices:
𝑥2
64
Co-Vertices:
y
y
y
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2
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1
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–1
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–2
–1
–1
x
–2
–2
–3
–3
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–5
–5
Conics Packet
1
2
3
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5
x
–5
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–2
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–1
1
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3
Rev A
4
5
x
Name:
Hyperbola
Score: ____/18
____/6 Find the equation of a hyperbola with the given a and c values. Assume that the transverse axis is
horizontal.
34. a=7 c = 9
35. a = 5 c = 15
36. a = 67 c = 92
37. a = 8 c = 20
38. a = 6 c = 8
39. a = 3 c = 7
____/12 Find the foci, vertices and asymptotes of each hyperbola. Then draw the graph.
40. 4y2 -36x2 = 144
41. 121y2 -4x2 = 121
Focus:
Focus:
Vertices:
Vertices:
Asymptotes:
42.
𝑦2
25
−
𝑥2
16
=1
Focus:
Vertices:
Asymptotes:
y
Asymptotes:
y
y
5
5
4
4
3
3
2
2
1
1
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3
2
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–1
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x
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–1
–1
–2
–2
–3
–3
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–4
–5
–5
1
2
3
4
5
x
–5
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–3
–2
–1
–1
1
2
3
–2
–3
–4
–5
Conics Packet
4
Rev A
4
5
x
Name:
Translating Conic Sections
Score: ____/14
____/8 Identify the conic section represented by each equation by writing the equation in standard form. For a parabola,
give the vertex. For a circle, give its center and radius. For an ellipse or hyperbola, give its center and foci.
43. 3x2 + 6x+ 5y2 – 20y – 13 = 0
44. x2 -9y2 + 36y – 45 = 0
45. x2 - 8x+ y2 – 4y + 19 = 0
46. x2 - 10x- 4y2 + 24y – 15 = 0
47. 4x2 - 16x+ 4y2 – 16y – 4 = 0
48. x2 - 4x+ 4y2 + 8y = 0
49. x2 - 2x– y + 3 = 0
50. y2 + 2y – x + 3 = 0
____/6 Write an equation of a conic section with the given characteristics
51. Hyperbola with center (-4,5), one vertex(-4,7), one focus(-4,8)
52. Parabola with vertex (1,-2), x-intercept 3, and opens to right
53. Ellipse with center (-4,-5), endpoints of major and minor axes (-4,-7), (-4,-3), (-1, -5),(-7,-5)
54. Circle with center (-1,2) diameter 12
55. Hyperbola with vertices (0,2) and (4,2), foci(-1,2) and (5,2)
56. Ellipse with center (0,-2), vertical major axis of length 5, minor axis of length 3
Conics Packet
5
Rev A