The Equation of a Circle

Question 1

A circle is graphed with its center C marked. Which equation represents the circle?

Accepted Answer

(x + 3)^2 + (y - 4)^2 = 100

Answer

(x - 3)^2 + (y + 4)^2 = 100

Answer

(x + 3)^2 + (y - 4)^2 = 10

Answer

(x - 4)^2 + (y + 3)^2 = 100

Question 2

Which standard-form equation is equivalent to x² + y² - 6x + 0y - 135 = 0?

Accepted Answer

(x - 3)² + (y - 0)² = 144

Answer

(x + 3)² + (y - 0)² = 144

Answer

(x - 3)² + (y - 0)² = 135

Answer

(x + 6)² + (y - 0)² = 144

Question 3

A circle has equation (x + 6)² + (y + 2)² = 4. What are its center and radius?

Accepted Answer

center (-6, -2), radius 2

Answer

center (6, 2), radius 2

Answer

center (-6, -2), radius 4

Answer

center (6, 2), radius 4

Question 4

A circle has equation (x - 3)² + (y - 0)² = 25. What are its center and radius?

Accepted Answer

center (3, 0), radius 5

Answer

center (-3, 0), radius 5

Answer

center (3, 0), radius 25

Answer

center (-3, 0), radius 25

Question 5

Which standard-form equation is equivalent to x² + y² - 6x + 0y + 5 = 0?

Accepted Answer

(x - 3)² + (y - 0)² = 4

Answer

(x + 3)² + (y - 0)² = 4

Answer

(x - 3)² + (y - 0)² = 5

Answer

(x + 6)² + (y - 0)² = 4

Question 6

Which standard-form equation is equivalent to x² + y² + 12x + 4y + 15 = 0?

Accepted Answer

(x + 6)² + (y + 2)² = 25

Answer

(x - 6)² + (y - 2)² = 25

Answer

(x + 6)² + (y + 2)² = 15

Answer

(x - 12)² + (y - 4)² = 25

Question 7

A circle is graphed with its center C marked. Which equation represents the circle?

Accepted Answer

(x - 2)^2 + (y + 7)^2 = 64

Answer

(x + 2)^2 + (y - 7)^2 = 64

Answer

(x - 2)^2 + (y + 7)^2 = 8

Answer

(x + 7)^2 + (y - 2)^2 = 64

Question 8

A circle has equation (x - 5)² + (y - 1)² = 49. What are its center and radius?

Accepted Answer

center (5, 1), radius 7

Answer

center (-5, -1), radius 7

Answer

center (5, 1), radius 49

Answer

center (-5, -1), radius 49

Question 9

A circle has equation (x + 8)² + (y - 6)² = 81. What are its center and radius?

Accepted Answer

center (-8, 6), radius 9

Answer

center (8, -6), radius 9

Answer

center (-8, 6), radius 81

Answer

center (8, -6), radius 81

Question 10

A segment with its endpoints labeled is shown as a diameter of a circle. Which equation represents the circle?

Accepted Answer

(x - 8)^2 + (y - 7)^2 = 100

Answer

(x - 8)^2 + (y - 7)^2 = 400

Answer

(x + 8)^2 + (y + 7)^2 = 100

Answer

(x - 2)^2 + (y + 1)^2 = 100

Question 11

Use the circle on the coordinate plane, with its center C marked. Which equation represents the circle?

Accepted Answer

(x + 1)^2 + (y + 5)^2 = 64

Answer

(x - 1)^2 + (y - 5)^2 = 64

Answer

(x + 1)^2 + (y + 5)^2 = 8

Answer

(x + 5)^2 + (y + 1)^2 = 64

Question 12

Which standard-form equation is equivalent to x² + y² - 4x + 14y + 17 = 0?

Accepted Answer

(x - 2)² + (y + 7)² = 36

Answer

(x + 2)² + (y - 7)² = 36

Answer

(x - 2)² + (y + 7)² = 17

Answer

(x + 4)² + (y - 14)² = 36

Question 13

A circle has equation (x - 4)² + (y - 8)² = 36. What are its center and radius?

Accepted Answer

center (4, 8), radius 6

Answer

center (-4, -8), radius 6

Answer

center (4, 8), radius 36

Answer

center (-4, -8), radius 36

Question 14

The coordinate plane shows a circle with its center C marked. Which equation represents the circle?

Accepted Answer

(x + 4)^2 + (y - 9)^2 = 9

Answer

(x - 4)^2 + (y + 9)^2 = 9

Answer

(x + 4)^2 + (y - 9)^2 = 3

Answer

(x - 9)^2 + (y + 4)^2 = 9

Question 15

The endpoints of a diameter of a circle are (-2, -6) and (22, 4). Which equation represents the circle?

Accepted Answer

(x - 10)² + (y + 1)² = 169

Answer

(x - 10)² + (y + 1)² = 676

Answer

(x + 10)² + (y - 1)² = 169

Answer

(x + 2)² + (y + 6)² = 169

Question 16

The endpoints of a diameter of a circle are (5, -4) and (21, 8). Which equation represents the circle?

Accepted Answer

(x - 13)² + (y - 2)² = 100

Answer

(x - 13)² + (y - 2)² = 400

Answer

(x + 13)² + (y + 2)² = 100

Answer

(x - 5)² + (y + 4)² = 100

Question 17

A circle with center C is shown on the grid. Which equation represents the circle?

Accepted Answer

(x - 0)^2 + (y - 3)^2 = 49

Answer

(x - 0)^2 + (y + 3)^2 = 49

Answer

(x - 0)^2 + (y - 3)^2 = 7

Answer

(x - 3)^2 + (y - 0)^2 = 49

Question 18

Which standard-form equation is equivalent to x² + y² - 14x + 6y + 42 = 0?

Accepted Answer

(x - 7)² + (y + 3)² = 16

Answer

(x + 7)² + (y - 3)² = 16

Answer

(x - 7)² + (y + 3)² = 42

Answer

(x + 14)² + (y - 6)² = 16

Question 19

A circle has equation (x - 4)² + (y - 8)² = 49. What are its center and radius?

Accepted Answer

center (4, 8), radius 7

Answer

center (-4, -8), radius 7

Answer

center (4, 8), radius 49

Answer

center (-4, -8), radius 49

Question 20

The graphed segment gives the endpoints of a circle's diameter. Which equation represents the circle?

Accepted Answer

(x - 7)^2 + (y - 4)^2 = 25

Answer

(x - 7)^2 + (y - 4)^2 = 100

Answer

(x + 7)^2 + (y + 4)^2 = 25

Answer

(x - 3)^2 + (y - 1)^2 = 25

Question 21

A circle has center (5, 1) and radius 5. Which equation represents the circle?

Accepted Answer

(x - 5)^2 + (y - 1)^2 = 25

Answer

(x + 5)^2 + (y + 1)^2 = 25

Answer

(x - 5)^2 + (y - 1)^2 = 5

Answer

(x - 1)^2 + (y - 5)^2 = 25

Question 22

The figure shows a circle and its center C on the coordinate plane. Which equation represents the circle?

Accepted Answer

(x + 8)^2 + (y - 6)^2 = 144

Answer

(x - 8)^2 + (y + 6)^2 = 144

Answer

(x + 8)^2 + (y - 6)^2 = 12

Answer

(x - 6)^2 + (y + 8)^2 = 144

Question 23

A circle has equation (x + 1)² + (y + 5)² = 64. What are its center and radius?

Accepted Answer

center (-1, -5), radius 8

Answer

center (1, 5), radius 8

Answer

center (-1, -5), radius 64

Answer

center (1, 5), radius 64

Question 24

A circle has equation (x - 2)² + (y + 7)² = 25. What are its center and radius?

Accepted Answer

center (2, -7), radius 5

Answer

center (-2, 7), radius 5

Answer

center (2, -7), radius 25

Answer

center (-2, 7), radius 25

Question 25

A coordinate-plane diagram shows a circle with its center C marked. Which equation represents the circle?

Accepted Answer

(x + 1)^2 + (y + 5)^2 = 4

Answer

(x - 1)^2 + (y - 5)^2 = 4

Answer

(x + 1)^2 + (y + 5)^2 = 2

Answer

(x + 5)^2 + (y + 1)^2 = 4

Question 26

The circle in the graph has its center C marked. Which equation represents the circle?

Accepted Answer

(x + 6)^2 + (y + 2)^2 = 81

Answer

(x - 6)^2 + (y - 2)^2 = 81

Answer

(x + 6)^2 + (y + 2)^2 = 9

Answer

(x + 2)^2 + (y + 6)^2 = 81

Question 27

Use the circle and its center C on the coordinate plane. Which equation represents the circle?

Accepted Answer

(x - 7)^2 + (y + 3)^2 = 16

Answer

(x + 7)^2 + (y - 3)^2 = 16

Answer

(x - 7)^2 + (y + 3)^2 = 4

Answer

(x + 3)^2 + (y - 7)^2 = 16

Question 28

The endpoints of a circle's diameter are labeled on the graph. Which equation represents the circle?

Accepted Answer

(x - 4)^2 + (y - 6)^2 = 25

Answer

(x - 4)^2 + (y - 6)^2 = 100

Answer

(x + 4)^2 + (y + 6)^2 = 25

Answer

(x - 1)^2 + (y - 2)^2 = 25

Question 29

Which standard-form equation is equivalent to x² + y² - 8x - 16y + 64 = 0?

Accepted Answer

(x - 4)² + (y - 8)² = 16

Answer

(x + 4)² + (y + 8)² = 16

Answer

(x - 4)² + (y - 8)² = 64

Answer

(x + 8)² + (y + 16)² = 16

Question 30

Which standard-form equation is equivalent to x² + y² + 12x + 4y + 24 = 0?

Accepted Answer

(x + 6)² + (y + 2)² = 16

Answer

(x - 6)² + (y - 2)² = 16

Answer

(x + 6)² + (y + 2)² = 24

Answer

(x - 12)² + (y - 4)² = 16

Question 31

The endpoints of a diameter of a circle are (4, 7) and (14, 31). Which equation represents the circle?

Accepted Answer

(x - 9)² + (y - 19)² = 169

Answer

(x - 9)² + (y - 19)² = 676

Answer

(x + 9)² + (y + 19)² = 169

Answer

(x - 4)² + (y - 7)² = 169

Question 32

A diameter of a circle is graphed with its endpoints marked. Which equation represents the circle?

Accepted Answer

(x + 4)^2 + (y - 6)^2 = 25

Answer

(x + 4)^2 + (y - 6)^2 = 100

Answer

(x - 4)^2 + (y + 6)^2 = 25

Answer

(x + 7)^2 + (y - 2)^2 = 25

Question 33

A circle has equation (x - 0)² + (y - 3)² = 64. What are its center and radius?

Accepted Answer

center (0, 3), radius 8

Answer

center (0, -3), radius 8

Answer

center (0, 3), radius 64

Answer

center (0, -3), radius 64

Question 34

A circle has equation (x - 7)² + (y + 3)² = 25. What are its center and radius?

Accepted Answer

center (7, -3), radius 5

Answer

center (-7, 3), radius 5

Answer

center (7, -3), radius 25

Answer

center (-7, 3), radius 25

Question 35

A circle with center C appears on the coordinate plane. Which equation represents the circle?

Accepted Answer

(x + 3)^2 + (y - 4)^2 = 4

Answer

(x - 3)^2 + (y + 4)^2 = 4

Answer

(x + 3)^2 + (y - 4)^2 = 2

Answer

(x - 4)^2 + (y + 3)^2 = 4

Question 36

A circle has equation (x + 8)² + (y - 6)² = 49. What are its center and radius?

Accepted Answer

center (-8, 6), radius 7

Answer

center (8, -6), radius 7

Answer

center (-8, 6), radius 49

Answer

center (8, -6), radius 49

Question 37

The graph displays a circle with its center C marked. Which equation represents the circle?

Accepted Answer

(x - 2)^2 + (y + 7)^2 = 9

Answer

(x + 2)^2 + (y - 7)^2 = 9

Answer

(x - 2)^2 + (y + 7)^2 = 3

Answer

(x + 7)^2 + (y - 2)^2 = 9

Question 38

A circle has equation (x + 4)² + (y - 9)² = 25. What are its center and radius?

Accepted Answer

center (-4, 9), radius 5

Answer

center (4, -9), radius 5

Answer

center (-4, 9), radius 25

Answer

center (4, -9), radius 25

Question 39

The segment on the coordinate plane represents a diameter of a circle. Which equation represents the circle?

Accepted Answer

(x - 3)^2 + (y - 4)^2 = 25

Answer

(x - 3)^2 + (y - 4)^2 = 100

Answer

(x + 3)^2 + (y + 4)^2 = 25

Answer

(x - 0)^2 + (y - 0)^2 = 25

Question 40

Which standard-form equation is equivalent to x² + y² - 14x + 6y + 49 = 0?

Accepted Answer

(x - 7)² + (y + 3)² = 9

Answer

(x + 7)² + (y - 3)² = 9

Answer

(x - 7)² + (y + 3)² = 49

Answer

(x + 14)² + (y - 6)² = 9

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The Equation of a Circle

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The Equation of a Circle

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner