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circle equation 1. (𝑥 − 17)2+(y − 19)2 = 49 A circle in the xy-plane has the equation shown above. How long is the radius of the circle? Correct answer: 7 Difficulty level: 2 2. A circle in the xy-plane has the equation (x + 17.5)2 + (𝑦 − 15.3)2 = 18.1 Which of the following best describes the location of the center of the circle and the length of its radius? A. Center:(-17.5,15.3) Radius:√18.1 B. Center:(-17.5,15.3) Radius:18.1 C. Center:(17.5,-15.3) Radius: √18.1 D. Center:(17.5,-15.3) Radius:18.1 Correct answer: A Difficulty level: 2 3. A circle in the xy-plane has the equation: 3.5(x + 2.2)2 + 3.5(𝑦 − 11.1)2 − 21 = 0 What is the radius of the circle? Round the answer to the nearest tenth. Correct answer:2.4 Difficulty level:2 4. (x + 16)2 + (𝑦 − 25)2 = 36 A circle in the xy-plane has the equation shown above. Which of the following correctly describes the location of the center of the circle and the length of its radius? A. Center:(16,-25) Radius:6 B. Center:(-16,25) Radius:36 C. Center:(-16,25) Radius:6 D. Center:(16,-25) Radius:36 Correct answer:C Difficulty level:2 5. (x + 55)2 + (𝑦 − 11.5)2 = 121 A circle in the xy-plane has the equation shown above. What is the length of the diameter of the circle? Correct answer:22 Difficulty level:2 6.A circle in the xy-plane has its center at (44,-34) and radius√3 . Which of the following is an equation of the circle? A. (x + 34)2 + (𝑦 − 44)2 = 3

B. (x + 34)2 + (𝑦 − 44)2 = √3 C. (x − 44)2 + (𝑦 + 34)2 = 3 D. (x − 44)2 + (𝑦 + 34)2 = √3 Correct answer: C Difficulty level:2 7.A circle in the xy-plane has its center on the line y=1.If the point(2,3)lies on the circle and the radius is4, which of the following could be the center of the circle? A.(2,1) B.(2,-3) C.(4,1) D.(4,-1) Correct answer:A Difficulty level:2 2

3

8. A circle in the xy-plane has its center at(− 3 , − 4) and radius 5. Which of the following is an equation of the circle? 2

3

3

4

2

3

2

3

A. (x + )2 + (𝑦 + )2 = 5 B. (x − 3)2 + (𝑦 + 4)2 = 25 C. (x + 3)2 + (𝑦 − 4)2 = 25 2

D. (x + )2 + (𝑦 + 34)2 = 25 3

Correct answer:D Difficulty level:2 9.A circle with center M is graphed in the xy-plane below.

Which of the following is an equation of the circle? A. (x + 8)2 + 𝑦 2 = 100

B. (x + 8)2 + (𝑦 + 8)2 = 100 C. (x + 8)2 + (𝑦 − 6)2 = 100 D. (x + 8)2 + (𝑦 + 6)2 = 100 Correct answer:B Difficulty level:2 10.A circle in the xy-plane has the equation What is the center of the circle? A.(51,14) B.(7,10) C.(0,0) D.(0,7) Correct answer:D Difficulty level:2

x 2 + 𝑦 2 − 14𝑦 − 51 = 0

11.A circle in the xy-plane has its center at (11,12). If the point(13,14) lies on the circle, which of the following is an equation of the circle? A. x 2 + 𝑦 2 − 22𝑥 + 24𝑦 = −257 B. x 2 + 𝑦 2 + 22𝑥 − 24𝑦 = −257 C. x 2 + 𝑦 2 + 22𝑥 + 24𝑦 = −257 D. x 2 + 𝑦 2 − 22𝑥 − 24𝑦 = −257 Correct answer:D Difficulty level:2 12. A circle in the xy-plane has a center at (-32.7,-9.08) and a radius of√10 .Which of the following is an equation of the circle? A. (x + 32.7)2 + (𝑦 + 9.08)2 = √10 B. (x + 32.7)2 + (𝑦 + 9.08)2 = √20 C. (x + 32.7)2 + (𝑦 + 9.08)2 = 10 D. (x + 32.7)2 + (𝑦 + 9.08)2 = 100 Correct answer:C Difficulty level:3 13. (x + 20)2 + (𝑦 − 30)2 = 225 A circle in the xy-plane has the equation shown above. What is the y-coordinate of the center of the circle? Correct answer:30 Difficulty level:3 14.A circle in the xy-plane has its center at the point(-6,1). If the point (7,12) lies on the circle, what is the radius of the circle? Round the answer to the nearest tenth. Correct answer:17 Difficulty level:3 15. A circle in the xy-plane has the equation: 36x2 + 36𝑦 2 − 12𝑥-27y-8=0. How long is the radius of the circle? 5

A.8 25

B.64

2

C.9

√2

D. 3

Correct answer:A

Difficulty level:3

16.A circle in the xy-plane has its center at (-2.8,6.1) and radius 4.2. Which of the following is an equation of the circle? A. (x − 2.8)2 + (𝑦 + 6.1)2 = 17.64 B. (x + 2.8)2 + (𝑦 + 6.1)2 = 17.64 C. (x + 2.8)2 + (𝑦 − 6.1)2 = 17.64 D. (x − 2.8)2 + (𝑦 − 6.1)2 = 17.64 Correct answer:C Difficulty level:3 17.A circle in the xy-plane has the equation (x + 18.5)2 + (y − 3.1)2 = 71.What is the center of the circle? A.(-18.5,3.1) B.(18.5,-3.1) C.(-342.25,9.61) D.(342.25,-9.61) Correct answer:A Difficulty level:3 18.A circle in the xy-plane has its center on the line x=3. If the point (4,5) lies on the circle and the radius is√2, which of the following could be the center of the circle? A.(3,3) B.(3,4) C.(3,5) D.(3,7) Correct answer:B Difficulty level:3 19. A circle in the xy-plane contains the points(−1,1),(1,1), and (−1,−1). Which of the following is an equation of the circle? A.x 2 + B. C. D. Correct answer:A Difficulty level:3 20.A circle in the xy-plane has its center at the point (0.4,−0.3). If the point(6,5) lies on the circle, what is the diameter of the circle? Round the answer to the nearest tenth. A.7.7units B.15.4units C.59.5units D.119units

Correct answer:B

Difficulty level:3

21. A circle in the xy-plane has a center at(-100,221) and a diameter of 17. Which of the following is an equation of the circle? A. (x + 100) 2 + (𝑦 − 221)2 = 72.25 B. (x + 100) 2 + (𝑦 − 221)2 = 289 C. (x − 100) 2 + (𝑦 + 221)2 = 72.25 D. (x − 100) 2 + (𝑦 + 221)2 = 289 Correct answer:A Difficulty level:3 4

7 2

5

10

22.A circle in the xy-plane has the equation: (y − )2 + (𝑥 +

) − 30 = 0

What is the radius of the circle? Round the answer to the nearest tenth. Correct answer:5.5 Difficulty level:3 23.A circle in the xy-plane has the equation: How long is the diameter of the circle? Correct answer:32 Difficulty level:4

x 2 + 𝑦 2 − 22𝑥 + 30𝑦 + 90 = 0

24.A circle in the xy-plane has a diameter with endpoints at(0,3) and(−4,0). Which of the following is an equation of the circle? A. (x + 4)2 + (𝑦 − 3)2 =

5 4

3

25

2

2

B. (x − )2 + (𝑦 + 2)2 = 3

5

2

2

3

25

C. (x + 2)2 + (𝑦 − )2 = D. (x + 2)2 + (𝑦 − 2)2 =

4

Correct answer:D Difficulty level:4 25.A circle in the xy-plane has the equation: x 2 + 𝑦 2 − 10𝑥 + 32𝑦 + 272 = 0 Which of the following best describes the location of the center of the circle and the length of its radius? A. Center:(10,-32) Radius:4√7 B. Center:(-10,32) Radius: 4√17 C. Center:(-5,16) Radius:3 D. Center:(5,-16) Radius:3 Correct answer:D Difficulty level:4

26.A circle in the xy-plane has the equation 4x 2 + 4y 2 − 24𝑥 = 28.What is the diameter of the circle? Correct answer:8 Difficulty level:4 27.A circle in the xy-plane has a diameter with endpoints at(16,−25) and(4,13). Which of the following is an equation of the circle? A. (x + 6)2 + (𝑦 − 10)2 = 397 B. (x − 10)2 + (𝑦 − 6)2 = 1588 C. (x − 10)2 + (𝑦 + 6)2 = 1588 D. (x − 10)2 + (𝑦 + 6)2 =397 Correct answer:D Difficulty level:4 5

28.A circle in the xy-plane has its center at. If the point(0,6) lies on the circle, which of the following is an equation of the circle? 1

2

5

2

3

2

1

2

5

2

3

2

1

2

2

1

5

3

2

2

A. (x − )2 + (𝑦 + )2 = B. (x − )2 + (𝑦 − )2 =

C. (x − 2)2 + (𝑦 + 3)2 = 5 D. (x + )2 + (𝑦 − )2 =

Correct answer:A Difficulty level:4 29.A circle in the xy-plane has a diameter with endpoints at (-41,69) and(31,-85).Which of the following is an equation of the circle? A. (x + 41)2 + (𝑦 − 69)2 = 28900 B. (x + 5)2 + (𝑦 + 8)2 = 7225 C. (x − 31)2 + (𝑦 + 85)2 = 28900 D. (x + 10)2 + (𝑦 + 16)2 = 7225 Correct answer:B Difficulty level:4

30.A circle in the xy-plane has the equation:2x 2 + 2y 2 − 8𝑥 − 5𝑦 −

55 8

What is the diameter of the circle? Correct answer:6 Difficulty level:4 31.A circle in the x 2 +y 2 -6x-10y=2.What is the diameter of the circle? Correct answer:12 Difficulty level:4

=0

5

6

7

8

5

10

32.A circle in the xy-plane has a center at ( , − ) and a diameter of

,Which of the following is

an equation of the circle? 5

6

49

5

6

49

8

5

400

5

6

49

5

6

49

A. (x + 8)2 + (𝑦 − 5)2 = 100 B. (x + )2 + (𝑦 − )2 =

C. (x − 8)2 + (𝑦 + 5)2 = 100 D. (x − 8)2 + (𝑦 + 5)2 = 400 Correct answer:D Difficulty level:4 33.The diameter of a circle graphed in the xy-plane has endpoints at(−23,15) and(1,−55). Which of the following is an equation of the circle? A. (x + 23)2 + (𝑦 − 15)2 = 1369 B. (x + 23)2 + (𝑦 − 15)2 = 5476 C. (x + 11)2 + (𝑦 + 20)2 = 5476 D. (x + 11)2 + (𝑦 + 20)2 = 1369 Correct answer:C Difficulty level:4 34.A circle in the xy-plane has the equation: x 2+y 2 -10x+34y-527=0.If the y-coordinate of a point on the circle is−38, what is a possible x-coordinate? Correct answer:25 or -15 Difficulty level:4