Equations of Circles

Question 1

The graph shows a circle. What is its equation?

Accepted Answer

(x - 1)^2 + (y - 4)^2 = 36

Answer

(x + 1)^2 + (y + 4)^2 = 36

Answer

(x - 1)^2 + (y - 4)^2 = 6

Answer

(x + 1)^2 + (y - 4)^2 = 36

Question 2

What is the equation of the circle with center (-6, -5) and radius 12?

Accepted Answer

(x + 6)^2 + (y + 5)^2 = 144

Answer

(x - 6)^2 + (y - 5)^2 = 144

Answer

(x + 6)^2 + (y + 5)^2 = 12

Answer

(x - 6)^2 + (y + 5)^2 = 144

Question 3

What are the center and radius of the circle x^2 + y^2 - 10x - 4y + 13 = 0?

Accepted Answer

center (5, 2), radius 4

Answer

center (-5, -2), radius 4

Answer

center (5, 2), radius 16

Answer

center (-10, -4), radius 4

Question 4

A student states that the circle (x - 5)^2 + (y + 3)^2 = 64 has center (-5, 3) and radius 64. Which correction is right?

Accepted Answer

center (5, -3), radius 8

Answer

center (5, -3), radius 64

Answer

center (-5, 3), radius 8

Answer

center (-5, -3), radius 8

Question 5

A student states that the circle (x + 2)^2 + (y - 3)^2 = 36 has center (2, -3) and radius 36. Which correction is right?

Accepted Answer

center (-2, 3), radius 6

Answer

center (-2, 3), radius 36

Answer

center (2, -3), radius 6

Answer

center (2, 3), radius 6

Question 6

Use the graph. What are the center and radius of the circle?

Accepted Answer

center (1, -1), radius 8

Answer

center (-1, 1), radius 8

Answer

center (1, -1), radius 64

Answer

center (-1, 1), radius 64

Question 7

A circle has center (-5, 5) and passes through the point (7, 10). What is its equation?

Accepted Answer

(x + 5)^2 + (y - 5)^2 = 169

Answer

(x + 5)^2 + (y - 5)^2 = 13

Answer

(x - 7)^2 + (y - 10)^2 = 169

Answer

(x - 5)^2 + (y + 5)^2 = 169

Question 8

A circle has center (-2, 5) and passes through the point (6, 20). What is its equation?

Accepted Answer

(x + 2)^2 + (y - 5)^2 = 289

Answer

(x + 2)^2 + (y - 5)^2 = 17

Answer

(x - 6)^2 + (y - 20)^2 = 289

Answer

(x - 2)^2 + (y + 5)^2 = 289

Question 9

The graph shows a circle and its center. What is its equation?

Accepted Answer

(x + 6)^2 + (y - 2)^2 = 49

Answer

(x - 6)^2 + (y + 2)^2 = 49

Answer

(x + 6)^2 + (y - 2)^2 = 7

Answer

(x - 6)^2 + (y - 2)^2 = 49

Question 10

What are the center and radius of the circle (x - 3)^2 + (y - 2)^2 = 81?

Accepted Answer

center (3, 2), radius 9

Answer

center (-3, -2), radius 9

Answer

center (3, 2), radius 81

Answer

center (-3, -2), radius 81

Question 11

What are the center and radius of the circle x^2 + y^2 + 2x - 10y + 1 = 0?

Accepted Answer

center (-1, 5), radius 5

Answer

center (1, -5), radius 5

Answer

center (-1, 5), radius 25

Answer

center (2, -10), radius 5

Question 12

What are the center and radius of the circle (x + 2)^2 + (y - 4)^2 = 144?

Accepted Answer

center (-2, 4), radius 12

Answer

center (2, -4), radius 12

Answer

center (-2, 4), radius 144

Answer

center (2, -4), radius 144

Question 13

What are the center and radius of the circle (x - 6)^2 + (y + 2)^2 = 81?

Accepted Answer

center (6, -2), radius 9

Answer

center (-6, 2), radius 9

Answer

center (6, -2), radius 81

Answer

center (-6, 2), radius 81

Question 14

Use the graph. What are the center and radius of the circle?

Accepted Answer

center (3, -4), radius 7

Answer

center (-3, 4), radius 7

Answer

center (3, -4), radius 49

Answer

center (-3, 4), radius 49

Question 15

The graph shows a circle. What is its equation?

Accepted Answer

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

Answer

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

Answer

(x - 3)^2 + (y - 3)^2 = 5

Answer

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

Question 16

A student states that the circle (x + 1)^2 + (y + 5)^2 = 144 has center (1, 5) and radius 144. Which correction is right?

Accepted Answer

center (-1, -5), radius 12

Answer

center (-1, -5), radius 144

Answer

center (1, 5), radius 12

Answer

center (1, -5), radius 12

Question 17

A circle has center (2, -3) and passes through the point (6, 0). What is its equation?

Accepted Answer

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

Answer

(x - 2)^2 + (y + 3)^2 = 5

Answer

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

Answer

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

Question 18

What is the equation of the circle with center (3, -2) and radius 10?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 19

What are the center and radius of the circle (x - 5)^2 + (y - 2)^2 = 100?

Accepted Answer

center (5, 2), radius 10

Answer

center (-5, -2), radius 10

Answer

center (5, 2), radius 100

Answer

center (-5, -2), radius 100

Question 20

What are the center and radius of the circle x^2 + y^2 + 6x - 6y - 18 = 0?

Accepted Answer

center (-3, 3), radius 6

Answer

center (3, -3), radius 6

Answer

center (-3, 3), radius 36

Answer

center (6, -6), radius 6

Question 21

Use the graph. What are the center and radius of the circle?

Accepted Answer

center (-4, 2), radius 5

Answer

center (4, -2), radius 5

Answer

center (-4, 2), radius 25

Answer

center (4, -2), radius 25

Question 22

Use the graph. What are the center and radius of the circle?

Accepted Answer

center (-1, -5), radius 5

Answer

center (1, 5), radius 5

Answer

center (-1, -5), radius 25

Answer

center (1, 5), radius 25

Question 23

What are the center and radius of the circle (x + 3)^2 + (y - 6)^2 = 81?

Accepted Answer

center (-3, 6), radius 9

Answer

center (3, -6), radius 9

Answer

center (-3, 6), radius 81

Answer

center (3, -6), radius 81

Question 24

The graph shows a circle. What is its equation?

Accepted Answer

(x + 6)^2 + (y + 3)^2 = 4

Answer

(x - 6)^2 + (y - 3)^2 = 4

Answer

(x + 6)^2 + (y + 3)^2 = 2

Answer

(x - 6)^2 + (y + 3)^2 = 4

Question 25

A circle has center (-4, 4) and passes through the point (4, 19). What is its equation?

Accepted Answer

(x + 4)^2 + (y - 4)^2 = 289

Answer

(x + 4)^2 + (y - 4)^2 = 17

Answer

(x - 4)^2 + (y - 19)^2 = 289

Answer

(x - 4)^2 + (y + 4)^2 = 289

Question 26

What are the center and radius of the circle x^2 + y^2 - 12x - 10y + 25 = 0?

Accepted Answer

center (6, 5), radius 6

Answer

center (-6, -5), radius 6

Answer

center (6, 5), radius 36

Answer

center (-12, -10), radius 6

Question 27

The graph shows a circle and its center. What is its equation?

Accepted Answer

(x - 2)^2 + (y - 5)^2 = 49

Answer

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

Answer

(x - 2)^2 + (y - 5)^2 = 7

Answer

(x + 2)^2 + (y - 5)^2 = 49

Question 28

A circle has center (5, -6) and passes through the point (11, 2). What is its equation?

Accepted Answer

(x - 5)^2 + (y + 6)^2 = 100

Answer

(x - 5)^2 + (y + 6)^2 = 10

Answer

(x - 11)^2 + (y - 2)^2 = 100

Answer

(x + 5)^2 + (y - 6)^2 = 100

Question 29

What are the center and radius of the circle x^2 + y^2 + 6x + 8y + 16 = 0?

Accepted Answer

center (-3, -4), radius 3

Answer

center (3, 4), radius 3

Answer

center (-3, -4), radius 9

Answer

center (6, 8), radius 3

Question 30

What are the center and radius of the circle (x - 3)^2 + (y + 1)^2 = 81?

Accepted Answer

center (3, -1), radius 9

Answer

center (-3, 1), radius 9

Answer

center (3, -1), radius 81

Answer

center (-3, 1), radius 81

Question 31

A circle has center (5, 6) and passes through the point (11, 14). What is its equation?

Accepted Answer

(x - 5)^2 + (y - 6)^2 = 100

Answer

(x - 5)^2 + (y - 6)^2 = 10

Answer

(x - 11)^2 + (y - 14)^2 = 100

Answer

(x + 5)^2 + (y + 6)^2 = 100

Question 32

The graph shows a circle and its center. What is its equation?

Accepted Answer

(x + 4)^2 + (y - 6)^2 = 64

Answer

(x - 4)^2 + (y + 6)^2 = 64

Answer

(x + 4)^2 + (y - 6)^2 = 8

Answer

(x - 4)^2 + (y - 6)^2 = 64

Question 33

A student states that the circle (x - 5)^2 + (y - 3)^2 = 144 has center (-5, -3) and radius 144. Which correction is right?

Accepted Answer

center (5, 3), radius 12

Answer

center (5, 3), radius 144

Answer

center (-5, -3), radius 12

Answer

center (-5, 3), radius 12

Question 34

What are the center and radius of the circle x^2 + y^2 + 10x + 8y - 103 = 0?

Accepted Answer

center (-5, -4), radius 12

Answer

center (5, 4), radius 12

Answer

center (-5, -4), radius 144

Answer

center (10, 8), radius 12

Question 35

What are the center and radius of the circle x^2 + y^2 - 10x - 6y - 15 = 0?

Accepted Answer

center (5, 3), radius 7

Answer

center (-5, -3), radius 7

Answer

center (5, 3), radius 49

Answer

center (-10, -6), radius 7

Question 36

What are the center and radius of the circle x^2 + y^2 - 8x + 12y - 12 = 0?

Accepted Answer

center (4, -6), radius 8

Answer

center (-4, 6), radius 8

Answer

center (4, -6), radius 64

Answer

center (-8, 12), radius 8

Question 37

What are the center and radius of the circle x^2 + y^2 - 10x + 4y - 20 = 0?

Accepted Answer

center (5, -2), radius 7

Answer

center (-5, 2), radius 7

Answer

center (5, -2), radius 49

Answer

center (-10, 4), radius 7

Question 38

The graph shows a circle and its center. What is its equation?

Accepted Answer

(x + 1)^2 + (y - 3)^2 = 64

Answer

(x - 1)^2 + (y + 3)^2 = 64

Answer

(x + 1)^2 + (y - 3)^2 = 8

Answer

(x - 1)^2 + (y - 3)^2 = 64

Question 39

What is the equation of the circle with center (5, -5) and radius 11?

Accepted Answer

(x - 5)^2 + (y + 5)^2 = 121

Answer

(x + 5)^2 + (y - 5)^2 = 121

Answer

(x - 5)^2 + (y + 5)^2 = 11

Answer

(x + 5)^2 + (y + 5)^2 = 121

Question 40

What is the equation of the circle with center (-3, -4) and radius 11?

Accepted Answer

(x + 3)^2 + (y + 4)^2 = 121

Answer

(x - 3)^2 + (y - 4)^2 = 121

Answer

(x + 3)^2 + (y + 4)^2 = 11

Answer

(x - 3)^2 + (y + 4)^2 = 121

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Equations of Circles

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Equations of Circles

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