AnswersCR CCSS Math 2 S2 M2960OXAngle Relationships (Sec 10-1)

Equation of a Circle Answers

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1
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Distance formula:

Question illustration
Y
Yes, the distance from (3, 0) to (0, 0) is 3 units.
Y
Yes, the distance from (0, 0) to (2, ) is 3 units.
Option Y
N
No, the distance from (3, 0) to (2, ) is not 3 units.
Option N
N
No, the distance from (0, 0) to (2, ) is not 3 units.
Option N
2
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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

(
(x – 3)2 + (y – 2)2 = 42, so the center is (3, 2).
(
(x + 3)2 + (y + 2)2 = 42, so the center is (3, 2).
(
(x – 3)2 + (y – 2)2 = 42, so the center is (–3, –2).
(
(x + 3)2 + (y + 2)2 = 42, so the center is (–3, –2).
3

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

Question illustration
(
(x – 4)2 + y2 = 100
(
(x – 4)2 + y2 = 10
x
x2 + (y – 4)² = 10
x
x2 + (y – 4)² = 100
4

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

Question illustration
(
(x – 1)2 + (y + 1)2 = 16
(
(x – 1)2 + (y + 1)2 = 4
(
(x + 1)2 + (y –1)2 = 4
(
(x + 1)2 + (y – 1)2 = 16
5

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.

Question illustration
(
(h + x)2 + (k + y)2 = r2
(
(x – h)2 + (y – k)2 = r2
(
(k + x)2 + (h + y)2 = r2
(
(x – k)2 + (y – h)2 = r2
6

A sprinkler is designed to water a circular area that has a radius of 7 feet. The sprinkler is located at (0,0) on a lawn. A flowerbed is planted 3 feet east and 6 feet south of the sprinkler.Determine if the distance from the flowerbed to the sprinkler places the flowerbed on or within the circular area that this sprinkler can water.

N
No. The flowerbed is 18 feet away from the sprinkler, which is more than the 7-foot radius.
Y
Yes. The flowerbed is exactly 7 feet away from the sprinkler.
N
No. The flowerbed is 9 feet away from the sprinkler, which is more than the 7-foot radius.
Y
Yes. The flowerbed is √45 feet away from the sprinkler, which is less than the 7-foot radius.
7

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

2
2 units
3
3 units
4
4 units
5
5 units
8

Which point is on the circle centered at the origin with a radius of 5 units?Distance formula:

Question illustration
(
(2, )
Option (
(
(2, )
Option (
(
(2, 1)
(
(2, 3)
9

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

(
(–12, –2)
(
(–6, –1)
(
(6, 1)
(
(12, 2)
10

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

T
The radius is the constant term, z.
T
The radius is the constant term, z, divided by 2.
T
The radius is the square root of the constant term, z.
T
The radius is the square of the constant term, z.
11

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
12

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)
13

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
14

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
15

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
16

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)
17

On a coordinate plane, a circle has a center at (4, 5) and a radius of 3 units.

Question illustration
A
(x – 4)2 + (y – 5)2 = 2
B
(x – 4)2 + (y – 5)2 = 4
C
(x – 5)2 + (y – 4)2 = 2
D
(x – 5)2 + (y – 4)2 = 4
18

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

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