Chapter 10 Conics
Short Answer
Graph the equation. Describe the graph and its lines of symmetry.
1.
2.
3. Graph
. Find the domain and range.
4. This ellipse is being used for a design on a poster. Name the x-intercepts and y-intercepts of the graph.
y
8
6
4
2
–8
–6
–4
–2
2
4
6
8
x
–2
–4
–6
–8
5. Write an equation for a graph that is the set of all points in the plane that are equidistant from the point F(5, 0) and the
line x = –5.
6. Write an equation of a parabola with a vertex at the origin and a focus at (–2, 0).
7. A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe
is located 5 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of
the mirror. Assume that the parabola opens upward.
8. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.
9. Use the graph to write an equation for the parabola.
y
4
2
–4
–2
2
4
x
–2
–4
10. Identify the vertex, focus, and directrix of the graph of
.
11. Identify the vertex, focus and the directrix of the graph of
.
12. Write an equation of a circle with center (2, 4) and radius 4.
13. Write an equation for the translation of
, 6 units right and 8 units up.
14. Write an equation in standard form for the circle.
y
4
2
–4
–2
2
4
x
–2
–4
15. Write an equation in standard form of an ellipse that has a vertex at (–2, 0), a co-vertex at (0, –3), and is centered at
the origin.
16. An elliptical track has a major axis that is 70 yards long and a minor axis that is 44 yards long. Find an equation for
the track if its center is (0, 0) and the major axis is the x-axis.
Write an equation of an ellipse in standard form with the center at the origin and with the given
characteristics.
17.
vertices at (–5, 0) and (0, 4)
18. Find the foci of the ellipse with the equation
. Graph the ellipse.
19. Find the foci of the ellipse with the equation
. Graph the ellipse.
Graph the conic section.
20.
21. Find the foci of the graph
22. Find the foci of the graph
. Draw the graph.
. Draw the graph.
Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is
an ellipse or a hyperbola, give the center and foci.
23.
24.
25.
26.
27. Graph
.
28. Which is the equation of the parabola that has a vertex at the origin and a focus at (3, 0)?
Chapter 10 Conics
Answer Section
SHORT ANSWER
1.
y
8
6
4
2
–8 –6 –4 –2
–2
2
4
6
8
x
–4
–6
–8
The graph is a circle of radius 8. Its center is at the origin. Every line through the center is a line of symmetry.
2.
y
The graph is an ellipse. The center is at the origin. It has two lines of
8
6
4
2
–8 –6 –4 –2
–2
2
4
6
–4
–6
–8
symmetry, the x-axis and the y-axis.
8
x
y
3.
The domain is all real numbers.The range is
4
2
–4
–2
2
4
x
–2
–4
4.
5.
6.
7.
8.
9.
10. vertex (2, 2), focus (2, 8), directrix at y = –4
11. vertex (–3, 4), focus(–3, 10), directrix at y = –2
12.
13.
14.
15.
16.
17.
18. foci (0,
2 3)
.
y
8
6
4
2
–8 –6 –4 –2
–2
2
4
6
8
x
6
x
8
x
–4
–6
–8
19. foci
y
6
4
2
–6
–4
–2
2
4
–2
–4
–6
y
20.
8
6
4
2
–8 –6 –4 –2
–2
–4
–6
–8
21. (
58 , 0)
2
4
6
y
12
8
4
–12
–8
–4
4
8
12 x
–4
–8
–12
22.
,
y
10
8
6
4
2
–10 –8 –6 –4 –2
–2
2
4
6
8 10 x
–4
–6
–8
–10
23. ellipse with center (2, –2), foci at
24. parabola; vertex (–5, –4)
25. hyperbola with center (4, –3), foci at
26. circle; center (2, 5); radius = 4
y
27.
4
2
–4
–2
2
–2
–4
4
x
28.