Name______________________________________ Parent Signature________________________________________
Ch. 9 Conics
Please show all work on a separate sheet of paper.
____ 1.
a. (–3, 0)
b. (0, 3)
Find the focus of the parabola:
c. (0, –3)
d. (3, 0)
2. Sketch the graph of the equation
5. Identify the focus and directrix of
6. Identify the focus and directrix of
.
7. Identify the focus and the directrix
y
10
8. Sketch the graph of the parabola.
–10
10
9. Sketch the graph of the parabola.
x
10. Sketch the graph of the parabola.
–10
3. Sketch the graph of the equation
11. Write the standard form of the equation of the
parabola with its vertex at (0, 0) and focus at
.
.
y
10
–10
10
____ 12.
Write the standard form of the
equation of the parabola with its vertex at (0, 0) and
focus at
.
a.
c.
b.
d.
x
–10
1
What is the graph of the equation y =  x2?
3
c.
____ 4.
y
a.
y
10
13. Write the standard form of the equation of the
parabola with its vertex at (0, 0) and directrix
14. Write the standard form of the equation of the
10
parabola with its vertex at (0, 0) and directrix
10 x
–10
10 x
–10
–10
–10
Graph:
15.
y
10
y
b.
y
d.
10
10
10 x
–10
10 x
–10
–10
10 x
–10
–10
–10
.
____ 16.
a.
y
c.
10
____ 20.
Write the standard form of the
equation of the circle with radius 7 and center at (0, 0).
a.
c.
=7
+
=1
y
10
b.
–10
10
x
–10
–10
–10
10
x
10
–10
10
x
–10
–10
17. Sketch the graph of
22. Write the standard form of the equation of the
circle that passes through the point (3, 4) with its center
at the origin.
y
d
.
10
23. Write the standard form of the equation of the
circle that passes through the point (1, –6) with its
center at the origin.
Graph:
24.
.
____
a.
25.
y
y
c.
10
–10
18. Sketch the graph of
= 14
x
21. Write the standard form of the equation of the
circle that passes through the point (0, 1) with its center
at the origin.
–10
y
b
.
10
d.
= 49
x
10
10
–10
x
10
.
–10
y
b
.
10
–10
y
d
.
10
–10
19.
The pool at a park is circular. You want to find
the equation of the circle that is the boundary of the
pool. Find the equation if the area of the pool is 400
square feet and (0, 0) represents the center of the pool.
–10
x
10
–10
10
–10
x
____ 26.
a.
c.
31. Write an equation of the ellipse with a vertex at (9,
0), a co-vertex at (0, 5), and center at (0, 0).
32. Write an equation of the ellipse with a vertex at
(–8, 0), a co-vertex at (0, 4), and center at (0, 0).
33. A skating park has a track shaped like an ellipse. If
the length of the track is 66 m and the width of the
track is 42 m, find the equation of the ellipse.
b.
d.
34. Write an equation of the ellipse with a vertex at (5,
0), a focus at (4, 0), and center at (0, 0).
35. How is the equation of an ellipse like the equation
of a circle? How are the equations different?
36. Graph
27. Sketch the graph of
28. Sketch the graph of
29. Determine the foci and vertices of the graph of
.
____ 30. Write an equation & graph an ellipse with vertices
of (–3, 0) & (3, 0), and co-vertices (0, –5) & (0, 5).
a.
c.
b.
d.
____
37.
a.
c.
b
.
d
.
38. Graph the equation and identify the asymptotes:
y
44. Write the equation of the hyperbola with vertices
at
and foci at
10
–10
43. Write the equation of the hyperbola with vertices
at
& foci at
10
x
45. How is the equation of a vertical ellipse like the
equation of a vertical hyperbola? How are they
different?
46. Find the equation of the circle with center (2, –6)
and radius of 4.
–10
____
39. Find the vertices and the foci of the hyperbola.
40. Find the vertices and the foci of the hyperbola.
41. Find the asymptotes and sketch the hyperbola.
47. Find the center and radius of
a. center (1, –5); r = 16
b. center (1, –5); r = 4
c. center (–1, 5); r = 16
d. center (–1, 5); r = 4
48. Write the equation of the circle in standard form.
Identify the radius and center.
49. Write the equation of the circle in standard form.
Identify the radius and center.
50. Write the equation of the circle in standard form.
Identify the radius and center.
51. Classify the conic section as a circle, an ellipse, a
hyperbola, or a parabola.
52. Classify the conic section. If it is a circle, an ellipse,
or a hyperbola, find its center. If it is a parabola, find its
vertex.
42. Find the asymptotes and sketch the hyperbola.
53. Classify the conic section. If it is a circle, an ellipse, or a
hyperbola, find its center. If it is a parabola, find its
vertex.
Classify the conic section. If it is a circle, an ellipse, or a
hyperbola, find its center. If it is a parabola, find its
vertex.
54.
55.
Classify the conic section. If it is a circle, an ellipse, or a
hyperbola, find its center. If it is a parabola, find its
vertex.
56.
57.
____ 58.
Write an equation in standard form for the
ellipse with foci (7, 0) and (–7, 0) and y-intercepts of 6
and
a.
c.
b.
d.
____ 62.
Find an equation for the parabola with
focus at (3, –3) and vertex at (3, 1).
a.
c.
b.
d.
____ 63.
Write the equation of the parabola in
standard form.
a.
c.
b.
d.
64. Find an equation of the parabola with vertex at (–3,
1) and focus (–1, 1).
65. Write the equation in standard form and classify
the conic section.
Sketch the graph:
____
a.
59.
66.
Sketch the graph of
c.
b.
.
d.
60. Find an equation of the hyperbola with vertices at (–3,
2) and (3, 2) and foci at (–5, 2), (5, 2).
Which equation represents the graph below?
____ 61.
67.
Without using graphing technology, sketch the
parent graph and translate it to obtain a graph of
.
a.
c.
b.
d.
____ 68.
Without using graphing technology, sketch the
parent graph and translate it to obtain a graph of
.
a.
c.
____
71. Find an equation of the ellipse with vertices at
(–2, 2) and (4, 2), and co-vertices at (1, 4) and (1, 0).
72. Classify the conic section as a circle, an ellipse, a
hyperbola, or a parabola.
a. parabola
c. circle
b. hyperbola
d. ellipse
73. Write the equation in standard form, then sketch
the graph of the equation.
b
.
d
.
Write an equation for the graph. Assume the graph is a
transformation of the graph
69.
____ 70.
a.
c.
b.
d.
74.
Compare and contrast the standard form
equations of the four types of conic sections.
Ch. 9 Conics
Answer Section
1. ANS: D
2. ANS:
DIF:
DIF:
Level A
Level B
y
10
11.
12.
13.
ANS:
ANS: C
ANS:
DIF:
DIF:
DIF: Level B
Level B
Level B
14.
15.
ANS:
ANS:
DIF:
DIF:
Level B
Level B
y
10
–10
10
x
10 x
–10
–10
3. ANS:
DIF:
Level B
y
–10
10
–10
10
16.
17.
ANS: C
ANS:
DIF:
DIF:
Level A
Level B
18.
ANS:
DIF:
Level B
19.
ANS:
20.
21.
22.
23.
24.
ANS: B
ANS:
ANS:
ANS:
ANS:
DIF:
25.
26.
27.
ANS: B
ANS: C
ANS:
DIF: Level A
DIF: Level A
DIF: Level B
x
–10
4. ANS: D
DIF: Level A
5. ANS:
DIF: Level B
Directrix: x = 1 Focus: (–1, 0)
6. ANS:
DIF: Level B
Focus: (0, 3)
Directrix: y = –3
7. ANS:
DIF: Level B
Directrix:
Focus:
8. ANS:
DIF:
9. ANS:
10.
ANS:
Level B
DIF:
Level B
DIF:
Level B
DIF: Level B
DIF:
Level B
DIF: Level B
DIF: Level B
DIF: Level B
Level B
y
10
–10
28. ANS:
DIF:
10
x
Level B
–10
39.
ANS:
Vertices:
40.
29. ANS:
; foci = (0,
DIF:
Level B
33 )
Level B
31. ANS:
DIF:
Level B
32. ANS:
DIF:
Level B
vertices =
30. ANS: A
DIF:
33. ANS:
34. ANS:
Vertices:
41.
ANS:
Level B
Foci:
DIF:
Level B
Foci:
DIF:
Level B
DIF:
Level B
Asymptotes:
DIF: Level B
DIF:
Level B
35. ANS:
DIF: Level C
Sample answer: When written in standard form, the
equations have the same terms, one involving the
square of x and the other involving the square of y,
added together. In both equations, the values of h and k
indicate the center of the graph, and the values of a and
b indicate the vertices. The equations are different in
that the terms of the ellipse equation have
denominators (always two unequal numbers), while the
terms of the circle equation do not have denominators.
36. ANS:
DIF: Level B
37. ANS: C
DIF:
Level B
38. ANS:
DIF:
Level B
1
asymptotes: y =
x
2
ANS:
DIF:
42.
ANS:
Asymptotes:
43.
ANS:
DIF: Level B
44.
ANS:
DIF: Level B
45.
ANS:
DIF: Level C
Sample answer: When written in standard form, the
equations have the same terms, one involving the
square of x and the other involving the square of y. The
order of these terms is also the same, with the term
involving y coming first. In both equations, the values of
h and k indicate the center of the graph, and the values
of a and b indicate the vertices. The equations are
different in that the terms of the ellipse equation are
added, while the terms of the hyperbola equation are
subtracted.
46.
ANS:
47.
ANS: D
DIF: Level B
DIF:
Level B
48.
ANS:
DIF: Level B
Center: (2, –3) Radius: 2
49.
ANS:
72. ANS: B
73. ANS:
DIF:
Level B
DIF: Level B
DIF: Level B
Center: (4, –1) Radius: 3
50.
ANS:
DIF: Level B
Center: (–3, 3) Radius: 3
51. ANS: hyperbola
52. ANS: Ellipse
Center: (4, –2)
53. ANS: Hyperbola
Center: (–7, 8)
54. ANS: Parabola
Vertex: (–7, –3)
55. ANS: Hyperbola
56. ANS: Parabola
57. ANS: Ellipse
58. ANS: D
59. ANS:
DIF:
DIF:
Level B
Level B
DIF:
Level B
DIF:
Level B
DIF:
DIF:
DIF:
DIF:
DIF:
Level B
Level B
Level B
Level B
Level B
60. ANS:
61. ANS: C
62. ANS: D
63. ANS: A
DIF: Level B
DIF:
DIF:
DIF:
64. ANS:
(Forms may vary.)
65. ANS:
Level B
Level B
Level B
DIF: Level B
DIF:
Level B
; The figure is an ellipse.
66. ANS: D
67. ANS:
DIF:
DIF:
Level A
Level B
68. ANS: D
DIF:
Level A
69. ANS:
70. ANS: D
DIF:
DIF:
Level B
Level A
71. ANS:
DIF: Level B
74.
ANS:
DIF: Level C
The equation for a circle is similar to the equation for an
ellipse. If a = b in the equation for the ellipse, then the
graph becomes a circle. If the operation between the
terms in the ellipse equation is changed to subtraction,
then the graph becomes a hyperbola. The parabola is
the only conic with just one variable raised to the
second power. The ellipse, hyperbola, and circle have
two different variables each raised to the second
power. The ellipse and the hyperbola both have “= 1”
on one side of their standard form equation.