AnswersMath II CR S2 RS3Equation of a Circle

Equation of a Circle — Unit test Answers

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Mrs. Culland is finding the center of a circle whose equation is x2 + y2 + 6x + 4y – 3 = 0 by completing the square. Her work is shown.x2 + y2 + 6x + 4y – 3 = 0x2 + 6x + y2 + 4y – 3 = 0(x2 + 6x) + (y2 + 4y) = 3(x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4

A
(x – 3)2 + (y – 2)2 = 42, so the center is (3, 2).
B
(x + 3)2 + (y + 2)2 = 42, so the center is (3, 2).
C
(x – 3)2 + (y – 2)2 = 42, so the center is (–3, –2).
D
(x + 3)2 + (y + 2)2 = 42, so the center is (–3, –2).
2
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What is the center of a circle represented by the equation (x+9)2+(y−6)2=102?

A
(−9,6)
B
(−6,9)
C
(6,−9)
D
(9,−6)
3

On a coordinate plane, a circle has a center at (1, negative 2) and a radius of 4 units.

Question illustration
A
(x – 1)2 + (y + 1)2 = 16
B
(x – 1)2 + (y + 1)2 = 4
C
(x + 1)2 + (y –1)2 = 4
D
(x + 1)2 + (y – 1)2 = 16
4

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.x2 + (y – 3)2 = 36x2 + (y – 5)2 = 6(x – 4)² + y² = 36(x + 6)² + y² = 144x2 + (y + 8)2 = 36

A
x2 + (y – 3)2 = 36
B
x2 + (y – 5)2 = 6
C
(x – 4)² + y² = 36
D
(x + 6)² + y² = 144
E
x2 + (y + 8)2 = 36
5

Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?

A
(x – 9)2 + (y + 4)2 = 25
B
(x + 4)2 + (y – 9)2 = 25
C
(x – 9)2 + (y + 4)2 = 100
D
(x + 4)2 + (y – 9)2 = 100
6

Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?

A
(x – 3)2 + (y – 5)2 = 6
B
(x – 3)2 + (y – 5)2 = 36
C
(x + 3)2 + (y + 5)2 = 6
D
(x + 3)2 + (y + 5)2 = 36
7

What is the center of a circle whose equation is x2 + y2 – 12x – 2y + 12 = 0?

A
(–12, –2)
B
(–6, –1)
C
(6, 1)
D
(12, 2)
8

What is the center of a circle whose equation is x2 + y2 + 4x – 8y + 11 = 0?

A
(–2, 4)
B
(–4, 8)
C
(2, –4)
D
(4, –8)
9

Which equation represents a circle that contains the point (–2, 8) and has a center at (4, 0)?Distance formula:

Question illustration
A
(x – 4)2 + y2 = 100
B
(x – 4)2 + y2 = 10
C
x2 + (y – 4)² = 10
D
x2 + (y – 4)² = 100
10

Which equation represents a circle that contains the point (–5, –3) and has a center at (–2, 1)? Distance formula:

Question illustration
A
(x – 1)2 + (y + 2)2 = 25
B
(x + 2)2 + (y – 1)2 = 5
C
(x + 2)2 + (y – 1)2 = 25
D
(x – 1)2 + (y + 2)2 = 5

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