ID: 1
Honors Precaluculus
Name___________________________________
Conic Sections Review Worksheet
Date________________ Period____
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Use the information provided to write the standard form equation of each circle.
1) Center: ( , )
Point on Circle: ( ,
3) Center: ( , )
Point on Circle: ( ,
2) Center: ( , )
Point on Circle: ( ,
)
)
4) Three points on the circle:
( , ), ( , ), and ( , )
)
Use the information provided to write the general conic form equation of each circle.
5) Center: ( , )
Point on Circle: ( ,
6) Three points on the circle:
( , ), ( , ), and ( ,
)
)
Identify the center and radius of each. Then sketch the graph.
7) ( x
)
8) ( x
y
y
)
(y
)
y
x
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x
-1-
Worksheet by Kuta Software LLC
9) x
x
y
y
10)
x
x
y
y
y
y
x
x
Use the information provided to write the standard form equation of each ellipse.
11) Vertices: ( , ), ( ,
Foci: ( , ), ( , )
13) Vertices: ( ,
Foci: (
), (
15) Vertices: ( ,
Foci: (
), (
,
)
12) Vertices: (
Foci: ( ,
, )
, ), (
,
), (
,
)
,
)
14) Vertices: (
Foci: (
,
), (
,
)
,
), (
,
,
), (
), (
)
,
)
,
)
)
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-2-
Worksheet by Kuta Software LLC
Identify the center, vertices, co-vertices, and foci of each. Then sketch the graph.
16)
x
y
x
y
17)
y
x
y
x
y
y
x
x
Use the information provided to write the standard form equation of each hyperbola.
18) Vertices: ( , ), ( , )
Conjugate Axis is
units long
20) Foci: (
), (
,
Asymptotes: y
y
)
,
units long
21) Foci: (
, ), (
Asymptotes: y x
y
x
,
)
x
), (
,
Asymptotes: y
)
,
x
y
22) Foci: (
19) Vertices: ( , ), (
Conjugate Axis is
,
)
x
x
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-3-
Worksheet by Kuta Software LLC
Identify the vertices and foci of each. Then sketch the graph.
23)
(x
)
y
24)
x
y
y
y
x
25)
x
y
x
x
26) x
y
y
y
y
x
x
Use the information provided to write the vertex form equation of each parabola.
27) Vertex: ( ,
29) Vertex: (
31) Vertex: ( ,
), Directrix: y
,
), Directrix: y
28) Vertex: ( ,
), Directrix: x
30) Vertex: ( ,
), Directrix: y
), Directrix: y
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-4-
Worksheet by Kuta Software LLC
Identify the vertex, focus, and directrix of each. Then sketch the graph.
(x
32) y
)
33) y
(x
y
)
y
x
34) y
x
x
x
35) y
y
x
x
y
x
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x
-5-
Worksheet by Kuta Software LLC
ID: 1
Honors Precaluculus
Name___________________________________
Conic Sections Review Worksheet
Date________________ Period____
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Use the information provided to write the standard form equation of each circle.
1) Center: ( , )
Point on Circle: ( ,
(x
)
(y
)
)
)
(x
3) Center: ( , )
Point on Circle: ( ,
(x
2) Center: ( , )
Point on Circle: ( ,
(y
)
(y
)
)
4) Three points on the circle:
( , ), ( , ), and ( , )
)
(x
)
)
(y
)
Use the information provided to write the general conic form equation of each circle.
5) Center: ( , )
Point on Circle: ( ,
x
y
x
6) Three points on the circle:
( , ), ( , ), and ( ,
)
x
y
y
x
)
y
Identify the center and radius of each. Then sketch the graph.
7) ( x
)
8) ( x
y
y
Center: ( ,
Radius:
(y
)
y
)
x
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)
Center: ( ,
Radius:
)
x
-1-
Worksheet by Kuta Software LLC
9) x
x
y
y
10)
y
Center: (
Radius:
x
x
y
y
)
,
y
Center: (
Radius:
x
,
)
x
Use the information provided to write the standard form equation of each ellipse.
11) Vertices: ( , ), ( ,
Foci: ( , ), ( , )
(x
)
(y
13) Vertices: ( ,
Foci: (
(x
)
(x
)
(y
12) Vertices: (
Foci: ( ,
)
), (
(y
15) Vertices: ( ,
Foci: (
)
(x
, )
, ), (
,
)
(x
,
), (
,
)
,
)
), (
(y
14) Vertices: (
Foci: (
)
), (
)
,
,
,
), (
)
)
), (
,
(y
)
,
), (
,
)
,
)
)
)
)
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-2-
Worksheet by Kuta Software LLC
Identify the center, vertices, co-vertices, and foci of each. Then sketch the graph.
16)
x
y
x
y
17)
y
Center: ( , )
Vertices: ( , )
( , )
Co-vertices: ( ,
( ,
Foci: (
,
(
,
x
y
x
y
y
Center: ( ,
Vertices: ( ,
)
)
( , )
Co-vertices: ( , )
( , )
)
)
)
)
Foci: (
,
,
(
x
)
)
x
Use the information provided to write the standard form equation of each hyperbola.
18) Vertices: ( , ), ( , )
Conjugate Axis is
units long
x
(y
)
20) Foci: (
(x
), (
,
Asymptotes: y
)
)
(y
(x
), (
)
)
(y
,
)
)
,
)
x
y
(x
(y
units long
)
,
Asymptotes: y
)
)
,
21) Foci: (
, ), (
Asymptotes: y x
y
x
x
(y
22) Foci: (
)
,
x
y
(x
19) Vertices: ( , ), (
Conjugate Axis is
x
)
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-3-
Worksheet by Kuta Software LLC
Identify the vertices and foci of each. Then sketch the graph.
23)
(x
)
y
24)
y
Vertices: ( ,
Foci: (
x
y
y
)
( , )
)
)
,
,
(
Vertices: ( ,
Foci: (
x
y
,
)
x
x
26) x
y
)
,
(
x
25)
)
( , )
Vertices: ( ,
( ,
Foci: (
(
y
y
y
)
)
,
,
Vertices: ( ,
)
)
Foci: (
(
x
)
( , )
)
,
,
)
x
Use the information provided to write the vertex form equation of each parabola.
27) Vertex: ( ,
y
(x
(x
x
), Directrix: y
,
(x
), Directrix: x
(y
)
30) Vertex: ( ,
)
31) Vertex: ( ,
y
28) Vertex: ( ,
)
29) Vertex: (
y
), Directrix: y
y
(x
), Directrix: y
)
), Directrix: y
)
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-4-
Worksheet by Kuta Software LLC
Identify the vertex, focus, and directrix of each. Then sketch the graph.
(x
32) y
)
33) y
y
Vertex: (
Focus:
(
,
)
,
(x
)
y
Vertex: (
)
Focus:
Directrix: y
x
x
x
35) y
y
Vertex: (
Focus:
)
,
Directrix: y
x
34) y
(
)
,
(
,
)
,
)
x
x
y
Vertex: (
Focus:
Directrix: y
(
,
,
)
)
Directrix: y
x
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x
-5-
Worksheet by Kuta Software LLC