Ch. 9 – Conics Study Guide
____
Graph:
1. Find the focus of the parabola:
a. (–3, 0)
c. (0, –3)
b. (0, 3)
d. (3, 0)
2. Sketch the graph of the equation
14.
.
3. Identify the focus and the directrix of the
parabola given by
4. Write the standard form of the equation of the
parabola with its vertex at (0, 0) and focus at
.
15.
16.
Find the vertices and the foci of the
hyperbola.
17.
Write the equation of the hyperbola with
vertices at
and foci at
Graph:
5.
18.
Find the equation of the circle with center
(2, –6) and radius of 4.
6.
7. Write the standard form of the equation of the
circle that passes through the point (0, 1) with its
center at the origin.
8. Write the standard form of the equation of the
circle that passes through the point (3, 4) with its
center at the origin.
____
19.
Find the center and radius of
a. center (1, –5); r = 16 c. center (–1, 5); r = 16
b. center (1, –5); r = 4 d. center (–1, 5); r = 4
20.
Write the equation of the circle in
standard form. Identify the radius and center.
Graph:
9.
21.
Classify the conic section as a circle, an
ellipse, a hyperbola, or a parabola.
10.
11. Determine the foci and vertices of the graph of
22.
Classify the conic section as a circle, an
ellipse, a hyperbola, or a parabola.
.
12. Write an equation of the ellipse with a vertex at
(9, 0), a co-vertex at (0, 5), and center at (0, 0).
13. Write an equation of the ellipse with a vertex at
(5, 0), a focus at (4, 0), and center at (0, 0).
23.
Classify the conic section as a circle, an
ellipse, a hyperbola, or a parabola.
Sketch the graph:
24.
Ch. 9 – Conics Study Guide
25. Find an equation of the hyperbola with vertices at
(–3, 2) and (3, 2) and foci at (–5, 2), (5, 2).
26. Find an equation of the parabola with vertex at (–
3, 1) and focus (–1, 1).
27. Write the equation in standard form and classify
the conic section.
28. Find an equation of the ellipse with vertices at (–
2, 2) and (4, 2), and co-vertices at (1, 4) and (1, 0).
____ 29. Classify the conic section as a circle, an ellipse, a
hyperbola, or a parabola.
a. parabola
b. hyperbola
c. circle
d. ellipse
30. Write the equation in standard form, then sketch
the graph of the equation.
31. Find the points of intersection, if any, of the
graphs in the system.
32. Find the points of intersection, if any, of the
graphs in the system.
Solve:
____ 33.
a. {(0, 0), (3, )}
b. (3, ), ( , )}
c. {(0, ), ( , 0)}
d. {(0, 3), (3, 0)}
Ch. 9 – Conics Study Guide
Ch. 9 Test
Answer Section
1. ANS: D
2. ANS:
16. ANS:
DIF:
Vertices:
DIF:
DIF:
Level A
Level B
Level B
Foci:
17. ANS:
DIF: Level B
y
10
18. ANS:
19. ANS: D
20. ANS:
–10
10
DIF:
Directrix:
DIF:
DIF:
Level B
Level B
Center: (2, –3) Radius: 2
x
–10
3. ANS:
DIF: Level B
Level B
21. ANS: Hyperbola
22. ANS: Parabola
23. ANS: Ellipse
24.
ANS:
DIF:
DIF:
DIF:
DIF:
Level B
Level B
Level B
Level B
Focus:
4. ANS:
5. ANS:
DIF:
DIF:
Level B
Level B
y
10
10 x
–10
–10
6.
7.
8.
9.
10.
11.
ANS: C
ANS:
ANS:
ANS: B
ANS: C
ANS:
vertices =
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
; foci = (0,
Level A
Level B
Level B
Level A
Level A
Level B
33 )
12. ANS:
DIF:
Level B
13. ANS:
DIF:
Level B
14. ANS:
DIF:
Level B
15. ANS: C
DIF:
Level B
25. ANS:
DIF: Level B
26. ANS:
DIF: Level B
(Forms may vary.)
27. ANS:
DIF:
Level B
; The figure is an ellipse.
28. ANS:
29. ANS: B
30. ANS:
DIF: Level B
DIF:
DIF:
Level B
Level B
31. ANS: (0, 0), (–4, 4)
32. ANS:
,
DIF: Level A
DIF: Level A
33. ANS: D
Level B
DIF: