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Intermediate Algebra

# Chapter 11

Intermediate AlgebraChapter 11

## Try It

11.1

$d = 5 d = 5$

11.2

$d = 10 d = 10$

11.3

$d = 15 d = 15$

11.4

$d = 13 d = 13$

11.5

$d = 130 , d ≈ 11.4 d = 130 , d ≈ 11.4$

11.6

$d = 2 , d ≈ 1.4 d = 2 , d ≈ 1.4$

11.9

$x 2 + y 2 = 36 x 2 + y 2 = 36$

11.10

$x 2 + y 2 = 64 x 2 + y 2 = 64$

11.11

$( x − 2 ) 2 + ( y + 4 ) 2 = 49 ( x − 2 ) 2 + ( y + 4 ) 2 = 49$

11.12

$( x + 3 ) 2 + ( y + 5 ) 2 = 81 ( x + 3 ) 2 + ( y + 5 ) 2 = 81$

11.13

$( x − 2 ) 2 + ( y − 1 ) 2 = 25 ( x − 2 ) 2 + ( y − 1 ) 2 = 25$

11.14

$( x − 7 ) 2 + ( y − 1 ) 2 = 100 ( x − 7 ) 2 + ( y − 1 ) 2 = 100$

11.15

The circle is centered at $(3,−4)(3,−4)$ with a radius of 2.

11.16

The circle is centered at $(3,1)(3,1)$ with a radius of 4.

11.17

The circle is centered at $(0,0)(0,0)$ with a radius of 3.

11.18

The circle is centered at $(0,0)(0,0)$ with a radius of 5.

11.19

The circle is centered at $(3,4)(3,4)$ with a radius of 4.

11.20

The circle is centered at $(−3,1)(−3,1)$ with a radius of 3.

11.21

The circle is centered at $(−1,0)(−1,0)$ with a radius of 2.

11.22

The circle is centered at $(0,6)(0,6)$ with a radius of 5.

11.25

$y=2(x+1)2+3y=2(x+1)2+3$

11.26

$y=−2(x−2)2+1y=−2(x−2)2+1$

11.35

$x=3(y+1)2+4x=3(y+1)2+4$

11.36

$x=−4(y+2)2+4x=−4(y+2)2+4$

11.37

$y = − 1 20 ( x − 20 ) 2 + 20 y = − 1 20 ( x − 20 ) 2 + 20$

11.38

$y = − 1 5 x 2 + 2 x y = − 1 5 x 2 + 2 x$ $y = − 1 5 ( x − 5 ) 2 + 5 y = − 1 5 ( x − 5 ) 2 + 5$

11.43

$x 2 4 + y 2 25 = 1 x 2 4 + y 2 25 = 1$

11.44

$x 2 9 + y 2 4 = 1 x 2 9 + y 2 4 = 1$

11.49

$(x+1)26+(y−4)29=1(x+1)26+(y−4)29=1$

11.50

$(x−2)24+(y−3)216=1(x−2)24+(y−3)216=1$

11.51

$x 2 625 + y 2 600 = 1 x 2 625 + y 2 600 = 1$

11.52

$x 2 1225 + y 2 1000 = 1 x 2 1225 + y 2 1000 = 1$

11.61

$(x+1)216−(y−2)29=1(x+1)216−(y−2)29=1$

11.62

$(x+3)225−(y+1)216=1(x+3)225−(y+1)216=1$

11.63

circle ellipse parabola hyperbola

11.64

ellipse parabola circle hyperbola

11.69

No solution

11.70

$( − 4 5 , 6 5 ) , ( 0 , 2 ) ( − 4 5 , 6 5 ) , ( 0 , 2 )$

11.71

No solution

11.72

$( 4 9 , − 2 3 ) , ( 1 , 1 ) ( 4 9 , − 2 3 ) , ( 1 , 1 )$

11.73

$( −3 , 0 ) , ( 3 , 0 ) , ( −2 2 , −1 ) , ( 2 2 , −1 ) ( −3 , 0 ) , ( 3 , 0 ) , ( −2 2 , −1 ) , ( 2 2 , −1 )$

11.74

$( −1 , 0 ) , ( 0 , 1 ) , ( 0 , −1 ) ( −1 , 0 ) , ( 0 , 1 ) , ( 0 , −1 )$

11.75

$( −3 , −4 ) , ( −3 , 4 ) , ( 3 , −4 ) , ( 3 , 4 ) ( −3 , −4 ) , ( −3 , 4 ) , ( 3 , −4 ) , ( 3 , 4 )$

11.76

$( −2 , 0 ) , ( 2 , 0 ) ( −2 , 0 ) , ( 2 , 0 )$

11.77

4 and 6

11.78

$−18−18$ and 17

11.79

If the length is 12 inches, the width is 16 inches. If the length is 16 inches, the width is 12 inches.

11.80

If the length is 12 inches, the width is 9 inches. If the length is 9 inches, the width is 12 inches.

## Section 11.1 Exercises

1.

$d = 5 d = 5$

3.

13

5.

5

7.

13

9.

$76 . d = 3 5 , d ≈ 6.7 76 . d = 3 5 , d ≈ 6.7$

11.

$d = 68 , d ≈ 8.2 d = 68 , d ≈ 8.2$

13.

Midpoint: $(2,−4)(2,−4)$

15.

Midpoint: $(312,−112)(312,−112)$

17.

$x 2 + y 2 = 49 x 2 + y 2 = 49$

19.

$x 2 + y 2 = 2 x 2 + y 2 = 2$

21.

$( x − 3 ) 2 + ( y − 5 ) 2 = 1 ( x − 3 ) 2 + ( y − 5 ) 2 = 1$

23.

$( x − 1.5 ) 2 + ( y + 3.5 ) 2 = 6.25 ( x − 1.5 ) 2 + ( y + 3.5 ) 2 = 6.25$

25.

$( x − 3 ) 2 + ( y + 2 ) 2 = 64 ( x − 3 ) 2 + ( y + 2 ) 2 = 64$

27.

$( x − 4 ) 2 + ( y − 4 ) 2 = 8 ( x − 4 ) 2 + ( y − 4 ) 2 = 8$

29.

The circle is centered at $(−5,−3)(−5,−3)$ with a radius of 1.

31.

The circle is centered at $(4,−2)(4,−2)$ with a radius of 4.

33.

The circle is centered at $(0,−2)(0,−2)$ with a radius of 5.

35.

The circle is centered at $(1.5,2.5)(1.5,2.5)$ with a radius of $0.5.0.5.$

37.

The circle is centered at $(0,0)(0,0)$ with a radius of 8.

39.

The circle is centered at $(0,0)(0,0)$ with a radius of 2.

41.

Center: $(−1,−3),(−1,−3),$ radius: 1

43.

Center: $(2,−5),(2,−5),$ radius: 6

45.

Center: $(0,−3),(0,−3),$ radius: 2

47.

Center: $(−2,0),(−2,0),$ radius: = 2

49.

Answers will vary.

51.

Answers will vary.

## Section 11.2 Exercises

53.
55.
57.

$y=−(x−1)2−3y=−(x−1)2−3$

59.

$y=−2(x+1)2−3y=−2(x+1)2−3$

61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.

$x=(y+2)2−9x=(y+2)2−9$

83.

$x=−2(y+3)2+2x=−2(y+3)2+2$

85.

87.

89.

91.

$y = − 1 15 ( x − 15 ) 2 + 15 y = − 1 15 ( x − 15 ) 2 + 15$

93.

$y = − 1 10 ( x − 30 ) 2 + 90 y = − 1 10 ( x − 30 ) 2 + 90$

95.

Answers will vary.

97.

Answers will vary.

## Section 11.3 Exercises

99.
101.
103.
105.
107.
109.
111.

$x 2 9 + y 2 25 = 1 x 2 9 + y 2 25 = 1$

113.

$x 2 9 + y 2 16 = 1 x 2 9 + y 2 16 = 1$

115.
117.
119.
121.
123.

$(x−2)29+(y−3)225=1(x−2)29+(y−3)225=1$

125.

$y24+(x−3)225=1y24+(x−3)225=1$

127.
129.
131.
133.
135.
137.
139.

$x 2 400 + y 2 300 = 1 x 2 400 + y 2 300 = 1$

141.

$x 2 2500 + y 2 1275 = 1 x 2 2500 + y 2 1275 = 1$

143.

Answers will vary.

145.

Answers will vary.

## Section 11.4 Exercises

147.
149.
151.
153.
155.
157.
159.
161.
163.
165.
167.
169.

$(x−1)24−(y−1)29=1(x−1)24−(y−1)29=1$

171.

$(y−2)29−(x−1)29=1(y−2)29−(x−1)29=1$

173.

$(y+1)21−(x+2)29=1(y+1)21−(x+2)29=1$

175.

parabola circle hyperbola ellipse

177.
179.
181.
183.
185.

Answers will vary.

187.

Answers will vary.

## Section 11.5 Exercises

189.
191.
193.
195.
197.
199.
201.

$( −1 , 0 ) , ( 0 , 3 ) ( −1 , 0 ) , ( 0 , 3 )$

203.

$( 2 , 0 ) ( 2 , 0 )$

205.

$( 12 , −5 ) , ( 12 , 5 ) ( 12 , −5 ) , ( 12 , 5 )$

207.

No solution

209.

$( 0 , −4 ) , ( 1 , −3 ) ( 0 , −4 ) , ( 1 , −3 )$

211.

$( 3 , 4 ) , ( 5 , 0 ) ( 3 , 4 ) , ( 5 , 0 )$

213.

$( 0 , −4 ) , ( − 7 , 3 ) , ( 7 , 3 ) ( 0 , −4 ) , ( − 7 , 3 ) , ( 7 , 3 )$

215.

$( 0 , −2 ) , ( − 3 , 1 ) , ( 3 , 1 ) ( 0 , −2 ) , ( − 3 , 1 ) , ( 3 , 1 )$

217.

$( −2 , 0 ) , ( 1 , − 3 ) , ( 1 , 3 ) ( −2 , 0 ) , ( 1 , − 3 ) , ( 1 , 3 )$

219.

$( −2 , −4 ) , ( −2 , 4 ) , ( 2 , −4 ) , ( 2 , 4 ) ( −2 , −4 ) , ( −2 , 4 ) , ( 2 , −4 ) , ( 2 , 4 )$

221.

$( −4 , 0 ) , ( 4 , 0 ) ( −4 , 0 ) , ( 4 , 0 )$

223.

$( − 3 , 0 ) , ( 3 , 0 ) ( − 3 , 0 ) , ( 3 , 0 )$

225.

$( −2 , −3 ) , ( −2 , 3 ) , ( 2 , −3 ) , ( 2 , 3 ) ( −2 , −3 ) , ( −2 , 3 ) , ( 2 , −3 ) , ( 2 , 3 )$

227.

$( −1 , −3 ) , ( −1 , 3 ) , ( 1 , −3 ) , ( 1 , 3 ) ( −1 , −3 ) , ( −1 , 3 ) , ( 1 , −3 ) , ( 1 , 3 )$

229.

$−3−3$ and 14

231.

$−7−7$ and $−8−8$ or 8 and 7

233.

$−6−6$ and $−4−4$ or $−6−6$ and 4 or 6 and $−4−4$ or 6 and 4

235.

If the length is 11 cm, the width is 15 cm. If the length is 15 cm, the width is 11 cm.

237.

If the length is 10 inches, the width is 24 inches. If the length is 24 inches, the width is 10 inches.

239.

The length is 40 inches and the width is 30 inches. The TV will not fit Donnette’s entertainment center.

241.

Answers will vary.

243.

Answers will vary.

## Review Exercises

245.

$d = 3 d = 3$

247.

$d = 17 , d ≈ 4.1 d = 17 , d ≈ 4.1$

249.

$( 4 , 4 ) ( 4 , 4 )$

251.

$( 3 2 , − 7 2 ) ( 3 2 , − 7 2 )$

253.

$x 2 + y 2 = 7 x 2 + y 2 = 7$

255.

$( x + 2 ) 2 + ( y + 5 ) 2 = 49 ( x + 2 ) 2 + ( y + 5 ) 2 = 49$

257.

$( x − 2 ) 2 + ( y − 2 ) 2 = 8 ( x − 2 ) 2 + ( y − 2 ) 2 = 8$

259.

radius: 12, center: $(0,0)(0,0)$

261.

radius: 7, center: $(−2,−5)(−2,−5)$

263.

radius: 8, center: $(0,2)(0,2)$

265.
267.
269.

$y=2(x−1)2−4y=2(x−1)2−4$

271.

$y=−(x−6)2+1y=−(x−6)2+1$

273.
275.
277.

$x=(y+2)2+1x=(y+2)2+1$

279.

$x=−2(y−1)2+2x=−2(y−1)2+2$

281.

$y = − 1 9 x 2 + 10 3 x y = − 1 9 x 2 + 10 3 x$

283.
285.
287.

$x 2 36 + y 2 64 = 1 x 2 36 + y 2 64 = 1$

289.
291.
293.

$(x−3)24+(y−7)225=1(x−3)24+(y−7)225=1$

295.

$x29+(y−7)24=1x29+(y−7)24=1$

297.
299.
301.
303.
305.

$(x+1)216−(y−3)24=1(x+1)216−(y−3)24=1$

307.

$(y−1)216−(x−1)24=1(y−1)216−(x−1)24=1$

309.

hyperbola circle parabola ellipse

311.
313.
315.

$( −1 , 4 ) ( −1 , 4 )$

317.

No solution

319.

$( − 7 , 3 ) , ( 7 , 3 ) ( − 7 , 3 ) , ( 7 , 3 )$

321.

$( −3 , 0 ) , ( 0 , −2 ) , ( 0 , 2 ) ( −3 , 0 ) , ( 0 , −2 ) , ( 0 , 2 )$

323.

$−3−3$ and $−4−4$ or 4 and 3

325.

If the length is 14 inches, the width is 15 inches. If the length is 15 inches, the width is 14 inches.

## Practice Test

327.

distance: 10, midpoint: $(−7,−7)(−7,−7)$

329.

$x 2 + y 2 = 121 x 2 + y 2 = 121$

331.

$( x + 2 ) 2 + ( y − 3 ) 2 = 52 ( x + 2 ) 2 + ( y − 3 ) 2 = 52$

333.

ellipse

335.

circle

337.

ellipse

339.

hyperbola

341.

circle
$(x+5)2+(y+3)2=4(x+5)2+(y+3)2=4$

343.

hyperbola
$(x−2)225−(y+1)29=1(x−2)225−(y+1)29=1$

345.

No solution

347.

$( 0 , −3 ) , ( 0 , 3 ) ( 0 , −3 ) , ( 0 , 3 )$

349.

$x 2 2025 + y 2 1400 = 1 x 2 2025 + y 2 1400 = 1$

351.

The length is 44 inches and the width is 33 inches. The TV will fit Olive’s entertainment center.

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