c. tion set is h 135 Section 1.2 Circles ts fy the Practice Exercises Prerequisite Review For Exercises R. 1-R.2, find the value of n so that the expression is a perfect square trinomial. Then factor the trinomial. SECTION 1.2 2 R.4. Multiply by using the special case products. Simplify. (x 2)2 R.2. x are. Note 8c +n R.1. c . (x-0f. R.3. Find the distance between (2, 3) and (-3, -2). Express your answer in simplified radical form. Concept Connections 1. A r. and is often denoted by is the set of all points in a plane equidistant from a fixed point called the ual 3. The standard form of an equation of a circle with center (h, k) and radius r is given by 4. An equation of a circle written in the form x y2+ Ax +By + C = 0 is called the equation of a circle. form of an 2. The distance from the center of a circle to any point on the circle is called the Objective 1: Write an Equation of a Circle in Standard Form 6. Is the point (3, 5) on the circle defined by 5. Is the point (2, 7) on the circle defined by (x 2) (- 7)24? 3)2 y5) 36? (x 8. Is the point (2, -7) on the circle defined by (x 6)2(y + 1)2 100? 7. Is the point (-4, 7) on the circle defined by (x +1) - 3)2= 25? For Exercises 9-16, determine the center and radius of the circle. 10. (x 3) (y 11. 2(y2.5)2= 6.25 14. y 28 1)2 16 (y + 2) 81 9. (x4) 13. xy20 + 2.25 12. (x 1.5) + y 25 -) 3 81 3 x + 16. 9 5 1 + 15. 49 2 For Exercises 17-32, information about a circle is given. a. Write an equation of the circle in standard form. b. Graph the circle. (See Examples 1-2) 18. Center: -3, 2); Radius: 4 17. Center: (-2, 5); Radius: 1 otr 20. Center: (6, -2); Radius: 6 19. Center: (4, 1); Radius: 3 22. Center: (-5, -2); Radius: V21 21. Center: (-4, -3); Radius: V11 24. Center: (0, 0); Radius: 4.2 23. Center: (0, 0); Radius: 2.6 26. The endpoints of a diameter are (7, 3) and (5, -1). 25. The endpoints of a diameter are (-2, 4) and (6, -2). 28. The center is (3, 1) and another point on the circle is (6, 5). 27. The center is (-2, -1) and another point on the circle is (6, 5), 30. The center is (-2, -4) and the circle is tangent to t x-axis. 29. The center is (4, 6) and the circle is tangent to the y-axis. (Informally, a line is tangent to a circle if it touches the circle in exactly one point.) 32. The center is in Quadrant II, the radius is 3, and t circle is tangent to both the x- and y-axes. 31. The center is in Quadrant IV, the radius is 5, and the circle is tangent to both the x- and y-axes. 34. Write an equation that represents the set of point are 9 units from (-4, 16). 33. Write an equation that represents the set of points that are 5 units from (8, -11). 36. Write an equation of the circle that is tangent to axes with radius V11 and center in Quadrant I 35. Write an equation of the circle that is tangent to both axes with radius V7 and center in Quadrant I.

c. tion set is h 135 Section 1.2 Circles ts fy the Practice Exercises Prerequisite Review For Exercises R. 1-R.2, find the value of n so that the expression is a perfect square trinomial. Then factor the trinomial. SECTION 1.2 2 R.4. Multiply by using the special case products. Simplify. (x 2)2 R.2. x are. Note 8c +n R.1. c . (x-0f. R.3. Find the distance between (2, 3) and (-3, -2). Express your answer in simplified radical form. Concept Connections 1. A r. and is often denoted by is the set of all points in a plane equidistant from a fixed point called the ual 3. The standard form of an equation of a circle with center (h, k) and radius r is given by 4. An equation of a circle written in the form x y2+ Ax +By + C = 0 is called the equation of a circle. form of an 2. The distance from the center of a circle to any point on the circle is called the Objective 1: Write an Equation of a Circle in Standard Form 6. Is the point (3, 5) on the circle defined by 5. Is the point (2, 7) on the circle defined by (x 2) (- 7)24? 3)2 y5) 36? (x 8. Is the point (2, -7) on the circle defined by (x 6)2(y + 1)2 100? 7. Is the point (-4, 7) on the circle defined by (x +1) - 3)2= 25? For Exercises 9-16, determine the center and radius of the circle. 10. (x 3) (y 11. 2(y2.5)2= 6.25 14. y 28 1)2 16 (y + 2) 81 9. (x4) 13. xy20 + 2.25 12. (x 1.5) + y 25 -) 3 81 3 x + 16. 9 5 1 + 15. 49 2 For Exercises 17-32, information about a circle is given. a. Write an equation of the circle in standard form. b. Graph the circle. (See Examples 1-2) 18. Center: -3, 2); Radius: 4 17. Center: (-2, 5); Radius: 1 otr 20. Center: (6, -2); Radius: 6 19. Center: (4, 1); Radius: 3 22. Center: (-5, -2); Radius: V21 21. Center: (-4, -3); Radius: V11 24. Center: (0, 0); Radius: 4.2 23. Center: (0, 0); Radius: 2.6 26. The endpoints of a diameter are (7, 3) and (5, -1). 25. The endpoints of a diameter are (-2, 4) and (6, -2). 28. The center is (3, 1) and another point on the circle is (6, 5). 27. The center is (-2, -1) and another point on the circle is (6, 5), 30. The center is (-2, -4) and the circle is tangent to t x-axis. 29. The center is (4, 6) and the circle is tangent to the y-axis. (Informally, a line is tangent to a circle if it touches the circle in exactly one point.) 32. The center is in Quadrant II, the radius is 3, and t circle is tangent to both the x- and y-axes. 31. The center is in Quadrant IV, the radius is 5, and the circle is tangent to both the x- and y-axes. 34. Write an equation that represents the set of point are 9 units from (-4, 16). 33. Write an equation that represents the set of points that are 5 units from (8, -11). 36. Write an equation of the circle that is tangent to axes with radius V11 and center in Quadrant I 35. Write an equation of the circle that is tangent to both axes with radius V7 and center in Quadrant I.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter8: Polynomials

Section8.7: Factoring Special Products

Problem 60PFA

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13,19,21

c.
tion set is h
135
Section 1.2 Circles
ts
fy the
Practice Exercises
Prerequisite Review
For Exercises R. 1-R.2, find the value of n so that the expression is a perfect square trinomial. Then factor the trinomial.
SECTION 1.2
2
R.4. Multiply by using the special case products.
Simplify. (x 2)2
R.2. x
are. Note
8c +n
R.1. c
. (x-0f.
R.3. Find the distance between (2, 3) and (-3, -2).
Express your answer in simplified radical form.
Concept Connections
1. A
r.
and is often denoted by
is the set of all points in a plane equidistant from a fixed point called the
ual
3. The standard form of an equation of a circle with center (h, k) and radius r is given by
4. An equation of a circle written in the form x y2+ Ax +By + C = 0 is called the
equation of a circle.
form of an
2. The distance from the center of a circle to any point on the circle is called the
Objective 1: Write an Equation of a Circle in Standard Form
6. Is the point (3, 5) on the circle defined by
5. Is the point (2, 7) on the circle defined by
(x 2) (- 7)24?
3)2 y5) 36?
(x
8. Is the point (2, -7) on the circle defined by
(x 6)2(y + 1)2 100?
7. Is the point (-4, 7) on the circle defined by
(x +1) - 3)2= 25?
For Exercises 9-16, determine the center and radius of the circle.
10. (x 3) (y
11. 2(y2.5)2= 6.25
14. y 28
1)2 16
(y + 2) 81
9. (x4)
13. xy20
+
2.25
12. (x 1.5) + y
25
-)
3
81
3
x +
16.
9
5
1
+
15.
49
2
For Exercises 17-32, information about a circle is given.
a. Write an equation of the circle in standard form.
b. Graph the circle. (See Examples 1-2)
18. Center: -3, 2); Radius: 4
17. Center: (-2, 5); Radius: 1
otr
20. Center: (6, -2); Radius: 6
19. Center: (4, 1); Radius: 3
22. Center: (-5, -2); Radius: V21
21. Center: (-4, -3); Radius: V11
24. Center: (0, 0); Radius: 4.2
23. Center: (0, 0); Radius: 2.6
26. The endpoints of a diameter are (7, 3) and (5, -1).
25. The endpoints of a diameter are (-2, 4) and (6, -2).
28. The center is (3, 1) and another point on the circle
is (6, 5).
27. The center is (-2, -1) and another point on the circle
is (6, 5),
30. The center is (-2, -4) and the circle is tangent to t
x-axis.
29. The center is (4, 6) and the circle is tangent to the
y-axis. (Informally, a line is tangent to a circle if it
touches the circle in exactly one point.)
32. The center is in Quadrant II, the radius is 3, and t
circle is tangent to both the x- and y-axes.
31. The center is in Quadrant IV, the radius is 5, and the
circle is tangent to both the x- and y-axes.
34. Write an equation that represents the set of point
are 9 units from (-4, 16).
33. Write an equation that represents the set of points that
are 5 units from (8, -11).
36. Write an equation of the circle that is tangent to
axes with radius V11 and center in Quadrant I
35. Write an equation of the circle that is tangent to both
axes with radius V7 and center in Quadrant I.

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