AnswersCR CCSS Math 2 S2 M2960OXSpecial Segments

Equation of a Circle Answers

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What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?

A
2 units
B
3 units
C
4 units
D
5 units
2
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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
3

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
4

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
5

Distance formula:

Question illustration
A
Yes, the distance from (–2, 4) to (1, ) is 4 units.
Option A
B
Yes, the distance from (–2, 0) to (1, ) is 4 units.
Option B
C
No, the distance from (–2, 0) to (1, ) is not 4 units.
Option C
D
No, the distance from (–2, 4) to (1, ) is not 4 units.
Option D
6

Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z?

A
The radius is the constant term, z.
B
The radius is the constant term, z, divided by 2.
C
The radius is the square root of the constant term, z.
D
The radius is the square of the constant term, z.
7

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

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
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

Distance formula:

Question illustration
A
Yes, the distance from (3, 0) to (0, 0) is 3 units.
B
Yes, the distance from (0, 0) to (2, ) is 3 units.
Option B
C
No, the distance from (3, 0) to (2, ) is not 3 units.
Option C
D
No, the distance from (0, 0) to (2, ) is not 3 units.
Option D
10

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)

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