Quiz about Equations of Circles

Question 1

Write the equation of a circle with center (7, 0) with radius 3.

Accepted Answer

(x - 7)² + y² = 9

Answer

x² + (y -7)² = 9

Answer

(x - 7)² + y² = 3

Answer

x² + (y -7)² = 3

Question 2

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

Accepted Answer

2

Answer

4

Answer

3

Answer

16

Question 3

In the equation (x+2)²+(y+3)²=49, the center of the circle is at....

Accepted Answer

(-2, -3)

Answer

(2, 3)

Answer

(3, 2)

Answer

(-3, -2)

Question 4

Question 4.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 5

Change the following equation to standard form
x²+y²-4x+12y-8=0

Accepted Answer

(x-2)²+(y+6)²=48

Answer

(x-2)²+(y-6)²=48

Answer

(x-6)²+(y-2)²=48

Answer

(x+2)²+(y-6)²=48

Question 6

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

Accepted Answer

Center (4,3)
Radius = 5 units

Answer

Center (4,3)
Radius = 25 units

Answer

Center (-4,-3)
Radius = 25 units

Answer

Center (-4,-3)
Radius = 5 units

Question 7

What is the equation of the circle, with centre (-2,-7) and radius 3 units?

Accepted Answer

(x + 2)² + (y + 7)² = 9

Answer

(x + 2)² + (y + 7)² = 3

Answer

(x - 2)² + (y - 7)² = 9

Answer

(x - 2)² + (y - 7)² = 3

Question 8

What is the equation of the circle, with center (-4,5) and radius 6 units?

Accepted Answer

(x + 4)² + (y - 5)² = 36

Answer

(x - 4)² + (y + 5)² = 6

Answer

(x - 4)² + (y + 5)² = 36

Answer

(x + 4)² + (y - 5)² = 6

Question 9

What is the coordinates of the center and the radius of the circle with equation:
(x + 7)² + (y - 6)² = 64 ?

Accepted Answer

Centre (-7,6)
Radius = 8 units

Answer

Centre (7,-6)
Radius = 8 units

Answer

Centre (-7,6)
Radius = 64 units

Answer

Centre (7,-6)
Radius = 64 units

Question 10

Write the equation of a circle with center (7, 0) with radius 3.

Accepted Answer

(x - 7)² + y² = 9

Answer

x² + (y -7)² = 9

Answer

(x - 7)² + y² = 3

Answer

x² + (y -7)² = 3

Question 11

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

Accepted Answer

2

Answer

4

Answer

3

Answer

16

Question 12

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

Accepted Answer

Center (4,3)
Radius = 5 units

Answer

Center (4,3)
Radius = 25 units

Answer

Center (-4,-3)
Radius = 25 units

Answer

Center (-4,-3)
Radius = 5 units

Question 13

In the equation (x-4)²+(x-3)²=25, the radius is

Accepted Answer

5

Answer

4

Answer

3

Answer

25

Question 14

What is the equation of the circle, with centre (3,8) and radius 4 units?

Accepted Answer

(x - 3)² + (y - 8)² = 16

Answer

(x - 3)² + (y - 8)² = 4

Answer

(x + 3)² + (y + 8)² = 16

Answer

(x + 3)² + (y + 8)² = 4

Question 15

What is the center and radius for a circle with the equation:
(x-4)²+(y+2)²=25

Accepted Answer

C:(4, -2), r=5

Answer

C:(-4, 2), r=5

Answer

C:(4, -2), r=25

Answer

C:(-4, 2), r=25

Question 16

Write the equation of a circle with center (7, 0) with radius 3.

Accepted Answer

(x - 7)² + y² = 9

Answer

x² + (y -7)² = 9

Answer

(x - 7)² + y² = 3

Answer

x² + (y -7)² = 3

Question 17

What are the coordinates of the center and the radius of the circle with an equation:
(x + 7)² + (y - 6)² = 64 ?

Accepted Answer

Centre (-7,6)
Radius = 8 units

Answer

Centre (7,-6)
Radius = 8 units

Answer

Centre (-7,6)
Radius = 64 units

Answer

Centre (7,-6)
Radius = 64 units

Question 18

What is the equation of the circle?

Accepted Answer

(x+1)² + (y +1)² = 9

Answer

(x+1)² + (y +1)² = 3

Answer

(x+1)² + (y -1)² = 3

Answer

(x-1)² + (y -1)² = 9

Question 19

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

Accepted Answer

Center (4,3)
Radius = 5 units

Answer

Center (4,3)
Radius = 25 units

Answer

Center (-4,-3)
Radius = 25 units

Answer

Center (-4,-3)
Radius = 5 units

Question 20

A circle has the equation x² + y² - 12x + 8y + 3 = 0. Use completing the square to write the equation in standard form.

Accepted Answer

(x - 6)² + (y + 4)² = 49

Answer

(x + 4)² + (y - 6)² = 49

Answer

(x - 6)² + (y + 4)² = 55

Answer

x² + y² = 55

Question 21

What is the center of the circle with equation x² + y² = 1?

Accepted Answer

(0, 0)

Answer

(1, 1)

Answer

not enough information

Question 22

What is the equation of the circle?

Accepted Answer

(x+1)² + (y +1)² = 9

Answer

(x+1)² + (y +1)² = 3

Answer

(x+1)² + (y -1)² = 3

Answer

(x-1)² + (y -1)² = 9

Question 23

What is the center and the radius?

Accepted Answer

C(5,1)r=8

Answer

C(1,5)r=64

Answer

C(-5,-1)

r=64

Answer

C(-1,-5)

r=8

Question 24

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

Accepted Answer

(3,2)

Answer

(-3, -2)

Answer

(-2, -3)

Answer

(2, 3)

Question 25

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

Accepted Answer

2

Answer

4

Answer

3

Answer

16

Question 26

Change the following equation to standard form
x²+y²-4x+12y-8=0

Accepted Answer

(x-2)²+(y+6)²=48

Answer

(x-2)²+(y-6)²=48

Answer

(x-6)²+(y-2)²=48

Answer

(x+2)²+(y-6)²=48

Question 27

What is the center of the circle with equation x² + y² = 1?

Accepted Answer

(0, 0)

Answer

(1, 1)

Answer

not enough information

Question 28

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

Accepted Answer

(3,2)

Answer

(-3, -2)

Answer

(-2, -3)

Answer

(2, 3)

Question 29

What is the equation of a circle with radius 2 and center (3, 4)?

Accepted Answer

(x-3)² + (y-4)² = 4

Answer

(x+3)² + (y+4)² = 2

Answer

(x-3)² + (y-4)² = 2

Answer

(x+3)² + (y+4)² = 4

Question 30

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

Accepted Answer

(3,2)

Answer

(-3, -2)

Answer

(-2, -3)

Answer

(2, 3)

Question 31

In the equation (x+2)²+(y+3)²=49, the center of the circle is at....

Accepted Answer

(-2, -3)

Answer

(2, 3)

Answer

(3, 2)

Answer

(-3, -2)

Question 32

What are the coordinates of the centre and the radius of the circle with equation:
(x + 3)² + (y + 1)² = 2² ?

Accepted Answer

Centre (-3,-1)
Radius = 2 units

Answer

Centre (-3,-1)
Radius = 4 units

Answer

Centre (3,1)
Radius = 2 units

Answer

Centre (3,1)
Radius = 4 units

Question 33

What is the center of the circle with equation x² + y² = 1?

Accepted Answer

(0, 0)

Answer

(1, 1)

Answer

not enough information

Question 34

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

Accepted Answer

2

Answer

4

Answer

3

Answer

16

Question 35

In the equation (x-3)²+(y+4)²=121, the radius of the circle is

Accepted Answer

11

Answer

242

Answer

121

Answer

22

Question 36

What is the equation of a circle with radius 2 and center (3, 4)?

Accepted Answer

(x-3)² + (y-4)² = 4

Answer

(x+3)² + (y+4)² = 2

Answer

(x-3)² + (y-4)² = 2

Answer

(x+3)² + (y+4)² = 4

Question 37

What is the equation of a circle with radius 4 and center (0, 8)?

Accepted Answer

x² + (y-8)² = 16

Answer

(x-8)² + y² = 4

Answer

x² + (y-8)² = 4

Answer

x² + (y+8)² = 16

Question 38

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

Accepted Answer

(x + 5)²+ (y - 2)²= 36

Answer

(x - 2)²+ (y + 5)²= 36

Answer

(x - 5)² + (y + 2)² = 6

Answer

(x + 2)²+ (y - 5)²= 6

Question 39

Which graph corresponds to
(x-8)²+ (y+2)²=

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 40

Which graph corresponds to
(x)²+ (y-6)²=9

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 41

Which graph corresponds to
(x+2)²+ (y-3)²=36

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 42

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

Accepted Answer

(x + 5)²+ (y - 2)²= 36

Answer

(x - 2)²+ (y + 5)²= 36

Answer

(x - 5)² + (y + 2)² = 6

Answer

(x + 2)²+ (y - 5)²= 6

Question 43

In the equation (x-3)²+(y+4)²=121, the radius of the circle is

Accepted Answer

11

Answer

242

Answer

121

Answer

22

Question 44

What is the center of the circle with equation x² + (y+6)² = 196?

Accepted Answer

(0, -6)

Answer

(1, 6)

Answer

(1, -6)

Answer

(0, 6)

Question 45

What is the radius of the circle with equation x² + (y+6)² = 196?

Accepted Answer

14

Answer

6

Answer

98

Answer

196

Question 46

Question 46.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 47

A line segment between two points on the circle which passes through the center

Accepted Answer

Diameter

Answer

Radius

Answer

Chord

Answer

Tangent

Question 48

What is the equation of the circle with the given information?

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 49

What is the center and radius of this image?

Accepted Answer

C(-3,5) ; r=4

Answer

C(3,-5) ; r=16

Answer

C(-3,5) ; r=16

Answer

C(3,-5) ; r=4

Question 50

In the equation
(x-3)²+(y-2)²=16, the center of the circle is...

Accepted Answer

(3,2)

Answer

(-3, -2)

Answer

(-2, -3)

Answer

(2, 3)

Question 51

See Picture

Accepted Answer

A

Answer

B

Answer

C

Question 52

Determine the center and radius: x²+ y²+ 14x - 2y = -1

Accepted Answer

center= (-7,1) radius= 7

Answer

center= (-7,2) radius= 3

Answer

center= (-4,1) radius= 5

Question 53

Determine the center and radius: x²+ y²+ 14x - 2y = -1

Accepted Answer

center= (-7,1) radius= 7

Answer

center= (-7,2) radius= 3

Answer

center= (-4,1) radius= 5

Question 54

Determine the center and radius:
x²+ y²- 10x + 8y -8 = 0

Accepted Answer

C = (5,-4) r = 7

Answer

C = (-5,4) r = 7

Answer

C = (-4,5) r = 49

Answer

C = (5,-4) r = 49

Question 55

What is the equation of this circle?

Accepted Answer

x² + (y + 2)² = 4

Answer

(x - 1)² + (y + 2)² = 2

Answer

x² + (y - 2)² = 4

Answer

x² + (y + 2)² = 2

Question 56

What is the equation of a circle with radius 2 and center (3, 4)?

Accepted Answer

(x-3)² + (y-4)² = 4

Answer

(x+3)² + (y+4)² = 2

Answer

(x-3)² + (y-4)² = 2

Answer

(x+3)² + (y+4)² = 4

Question 57

What is the equation of this circle?

Accepted Answer

(x + 3)² + (y - 1)² = 9

Answer

(x - 3)² + (y + 1)² = 9

Answer

(x - 3)² + (y + 1)² = 3

Answer

(x + 3)² + (y - 1)² = 3

Question 58

What is the equation of this circle?

Accepted Answer

(x - 4)² + (y - 3)² = 1

Answer

(x + 4)²+(y + 3)² = 1

Answer

(x - 4)²+(y - 3)²=2

Answer

(x - 4)²+(y + 3)²=0.5

Question 59

What is the equation of this circle?

Accepted Answer

(x + 2)²+(y + 1)²=16

Answer

(x - 2)² + (y - 1)² = 4

Answer

(x + 2)² + (y - 1)² = 4

Answer

(x + 2)²+(y - 1)²=16

Question 60

Write the equation of the circle with center C( -5 , 8 ) and radius = 7

Accepted Answer

( x + 5 )² + ( y - 8 )² = 49

Answer

( x - 5 )² + ( y + 8 )² = 14

Answer

( x - 5 )² + ( y - 8 )² = 49

Answer

( x - 5 )² + ( y + 8 )² = 49

Question 61

Write the equation of the circle with center C( 4 , -8 ) and radius = 5

Accepted Answer

( x - 4 )² + ( y + 8 )² = 25

Answer

( x + 4 )² + ( y - 8 )² = 25

Answer

( x - 4 )² + ( y - 8 )² = 25

Answer

( x + 4 )² + ( y - 8 )² = 10

Question 62

Question 62.

Accepted Answer

(x+1)² + (y +1)² = 9

Answer

(x+1)² + (y +1)² = 3

Answer

(x+1)² + (y -1)² = 3

Answer

(x-1)² + (y -1)² = 9

Question 63

Determine the center and radius:
x²+ y²- 10x + 8y -8 = 0

Accepted Answer

C = (5,-4) r = 7

Answer

C = (-5,4) r = 7

Answer

C = (-4,5) r = 49

Answer

C = (5,-4) r = 49

Question 64

A circle has the equation x² + y² - 12x + 8y + 3 = 0. Use completing the square to write the equation in standard form.

Accepted Answer

(x - 6)² + (y + 4)² = 49

Answer

(x + 4)² + (y - 6)² = 49

Answer

(x - 6)² + (y + 4)² = 55

Answer

x² + y² = 55

Equations of Circles

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