Study Guide and Review - Chapter 9
State whether each sentence is true or false . If false, replace the underlined term to make a true
sentence.
1. The set of all points in a plane that are equidistant from a given point in the plane, called the focus, forms a circle.
SOLUTION: false, center
2. A(n) ellipse is the set of all points in a plane such that the sum of the distances from the two fixed points is constant.
SOLUTION: true
3. The endpoints of the major axis of an ellipse are the foci of the ellipse.
SOLUTION: false, vertices
4. The radius is the distance from the center of a circle to any point on the circle.
SOLUTION: true
5. The line segment with endpoints on a parabola, through the focus of the parabola, and perpendicular to the axis of
symmetry is called the latus rectum.
SOLUTION: true
6. Every hyperbola has two axes of symmetry, the transverse axis and the major axis.
SOLUTION: false, conjugate axis
7. A directrix is the set of all points in a plane that are equidistant from a given point in the plane, called the center
SOLUTION: false, circle
8. A hyperbola is the set of all points in a plane such that the absolute value of the sum of the distances from any point
on the hyperbola to two given points is constant.
SOLUTION: false; difference
9. A parabola can be defined as the set of all points in a plane that are the same distance from the focus and a given
line called the directrix.
SOLUTION: true
10. The major axis is the longer of the two axes of symmetry of an ellipse.
SOLUTION: true
Find the midpoint of the line segment with endpoints at the given coordinates.
6), (3, -4)
11. (–8,
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SOLUTION: Substitute –8, 3, 6 and 4 for x , x , y and y respectively in the midpoint formula.
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true
10. The major axis is the longer of the two axes of symmetry of an ellipse.
SOLUTION: Study
Guide and Review - Chapter 9
true
Find the midpoint of the line segment with endpoints at the given coordinates.
11. (–8, 6), (3, 4)
SOLUTION: Substitute –8, 3, 6 and 4 for x1, x2, y 1 and y 2 respectively in the midpoint formula.
13. SOLUTION: Substitute
for x1, x2, y 1 and y 2 respectively in the midpoint formula.
Find the distance between each pair of points with the given coordinates.
15. (10, –3), (1, –5)
SOLUTION: Substitute 10, 1 –3 and –5 for x1, x2, y 1 and y 2 respectively in the distance formula.
17. SOLUTION: Substitute
for x1, x2, y 1 and y 2 respectively in the distance formula.
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Study Guide and Review - Chapter 9
17. SOLUTION: Substitute
for x1, x2, y 1 and y 2 respectively in the distance formula.
Graph each equation.
21. SOLUTION: vertex:
axis of symmetry: x = –4.
focus:
directrix: x =
length of latus rectum: 3 unit
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23. Page 3
Study Guide and Review - Chapter 9
Graph each equation.
21. SOLUTION: vertex:
axis of symmetry: x = –4.
focus:
directrix: x =
length of latus rectum: 3 unit
opens up
23. SOLUTION: vertex: (–24, 7)
axis of symmetry: y = 7.
focus: (–23.75, 7)
directrix: x = –24.25
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length
of latus
rectum:
1 unit
opens to the right
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Study Guide and Review - Chapter 9
23. SOLUTION: vertex: (–24, 7)
axis of symmetry: y = 7.
focus: (–23.75, 7)
directrix: x = –24.25
length of latus rectum: 1 unit
opens to the right
Write each equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of
the parabola.
25. SOLUTION: vertex: (2, –7)
axis of symmetry: x = 2
opens up
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vertex: (2, –7)
axis of symmetry: x = 2
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Guide
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up and Review - Chapter 9
27. SOLUTION: vertex: (–29, –7)
axis of symmetry: y = –7
opens to the right
Write an equation for the circle that satisfies each set of conditions.
29. center (–1, 6), radius 3 units
SOLUTION: Substitute –1, 6 and 3 for h, k and d in the standard form of circle equation.
Find the center and radius of each circle. Then graph the circle.
35. SOLUTION: The center of the circle is (–2, 1).
The radius of the circle is 4.
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Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse
with the given equation. Then graph the ellipse.
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Study Guide and Review - Chapter 9
Find the center and radius of each circle. Then graph the circle.
35. SOLUTION: The center of the circle is (–2, 1).
The radius of the circle is 4.
Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse
with the given equation. Then graph the ellipse.
37. SOLUTION: Here, (h, k) = (0, 0), a = 6 and b = 3.
center:
foci:
length of the major axis: 12 units
length of the minor axis: 6 units
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Study Guide and Review - Chapter 9
Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse
with the given equation. Then graph the ellipse.
37. SOLUTION: Here, (h, k) = (0, 0), a = 6 and b = 3.
center:
foci:
length of the major axis: 12 units
length of the minor axis: 6 units
39. SOLUTION: Center: (h, k) = (0, 4)
Here a = 6 and b = 2.
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Study Guide and Review - Chapter 9
39. SOLUTION: Center: (h, k) = (0, 4)
Here a = 6 and b = 2.
center:
foci:
length of the major axis: 12 units
length of the minor axis: 4 units
41. SOLUTION: HereManual
a = 5- and
b =by
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center:
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Study Guide and Review - Chapter 9
41. SOLUTION: Here a = 5 and b = 4.
center:
foci:
length of the major axis: 10 units
length of the minor axis: 8 units
43. SOLUTION: Here a = 5 and b = 3.
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43. SOLUTION: Here a = 5 and b = 3.
center:
foci:
length of the major axis: 10 units
length of the minor axis: 6 units
Graph each hyperbola. Identify the vertices, foci, and asymptotes.
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Study Guide and Review - Chapter 9
Graph each hyperbola. Identify the vertices, foci, and asymptotes.
47. SOLUTION: The values of h, k, a and b are 3, –2, 1 and 2.
The vertices of the hyperbola are (2, –2) and (4, –2).
The foci are
.
The equations of the asymptotes are
.
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The values of h, k, a and b are 0, 0, 3 and 2.
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The vertices of the hyperbola are (2, –2) and (4, –2).
The foci are
.
Study
Guide
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- Chapterare
9
The
equations
of the asymptotes
.
49. SOLUTION: The values of h, k, a and b are 0, 0, 3 and 2.
The vertices of the hyperbola are (±3, 0).
The foci are
.
The equations of the asymptotes are
.
Write each equation in standard form. State whether the graph of the equation is a parabola, circle,
ellipse, or hyperbola. Then graph.
53. SOLUTION: Given equation is an ellipse.
Graph the function.
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The vertices of the hyperbola are (±3, 0).
The foci are
.
Study
Guide
and Review
- Chapterare
9
The
equations
of the asymptotes
.
Write each equation in standard form. State whether the graph of the equation is a parabola, circle,
ellipse, or hyperbola. Then graph.
53. SOLUTION: Given equation is an ellipse.
Graph the function.
Solve each system of equations.
61. SOLUTION: Solve the linear equation for y.
Substitute –x for y in the quadratic equation and solve for x.
Substitute the values of x in the linear equation and find the value of y.
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The solutions are (2, –2) and (–2, 2).
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Study Guide and Review - Chapter 9
Solve each system of equations.
61. SOLUTION: Solve the linear equation for y.
Substitute –x for y in the quadratic equation and solve for x.
Substitute the values of x in the linear equation and find the value of y.
The solutions are (2, –2) and (–2, 2).
63. SOLUTION: Solve the linear equation for y.
Substitute
for y in the quadratic equation and solve for x.
Substitute the values of x in the linear equation and find the value of y.
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The solution is (4, 0).
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Study
Guide
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Review
- Chapter
9
The
solutions
(2, –2)
and (–2, 2).
63. SOLUTION: Solve the linear equation for y.
Substitute
for y in the quadratic equation and solve for x.
Substitute the values of x in the linear equation and find the value of y.
The solution is (4, 0).
65. SOLUTION: Substitute the values of x in the first equation and find the values of y.
The solutions are (1, ±5), (–1, ±5).
Solve each system of inequalities by graphing.
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Guide and Review - Chapter 9
Study
The solutions are (1, ±5), (–1, ±5).
Solve each system of inequalities by graphing.
69. SOLUTION: 71. SOLUTION: 73. SOLUTION: eSolutions Manual - Powered by Cognero
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