Equation of a Circle — Quiz Answers

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1
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y -axis? Choose two correct answers.

A
x squared plus open paren y minus 5 close paren squared is equal to 6
B
x squared plus open paren y minus 3 close paren squared is equal to 36
C
open paren x minus 4 close paren squared plus y squared is equal to 36
D
open paren x plus 6 close paren squared plus y squared is equal to 144
E
x squared plus open paren y plus 8 close paren squared is equal to 36
2
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Which equation represents a circle with a center at negative 4 comma 9 and a diameter of 10 units?

A
open paren x minus 9 close paren squared plus open paren y plus 4 close paren squared is equal to 100
B
open paren x minus 9 close paren squared plus open paren y plus 4 close paren squared is equal to 25
C
open paren x plus 4 close paren squared plus open paren y minus 9 close paren squared is equal to 25
D
open paren x plus 4 close paren squared plus open paren y minus 9 close paren squared is equal to 100
5

Which explains how to find the radius of a circle whose equation is in the form x squared plus y squared is equal to z ?

A
The radius is the constant term, z , divided by 2 .
B
The radius is the constant term, z .
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 equation represents a circle that contains the point negative 5 comma negative 3 and has a center at negative 2 comma 1 ? Distance formula: square root of open paren x sub 2 minus x sub 1 close paren squared plus open paren y sub 2 minus y sub 1 close paren squared end root

A
open paren x plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 5
B
open paren x minus 1 close paren squared plus open paren y plus 2 close paren squared is equal to 25
C
open paren x minus 1 close paren squared plus open paren y plus 2 close paren squared is equal to 5
D
open paren x plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 25
9

Which equation represents a circle with a center at negative 3 comma negative 5 and a radius of 6 units?

A
open paren x minus 3 close paren squared plus open paren y minus 5 close paren squared is equal to 36
B
open paren x plus 3 close paren squared plus open paren y plus 5 close paren squared is equal to 6
C
open paren x minus 3 close paren squared plus open paren y minus 5 close paren squared is equal to 6
D
open paren x plus 3 close paren squared plus open paren y plus 5 close paren squared is equal to 36
10

Which equation represents a circle that contains the point negative 2 comma 8 and has a center at 4 comma 0 ? Distance formula: square root of open paren x sub 2 minus x sub 1 close paren squared plus open paren y sub 2 minus y sub 1 close paren squared end root

A
x squared plus open paren y minus 4 close paren squared is equal to 100
B
open paren x minus 4 close paren squared plus y squared is equal to 100
C
open paren x minus 4 close paren squared plus y squared is equal to 10
D
x squared plus open paren y minus 4 close paren squared is equal to 10
11

Which equation represents a circle with a center at negative 3 comma negative 5 and a radius of 6 units?

A
open paren x plus 3 close paren squared plus open paren y plus 5 close paren squared is equal to 36
B
open paren x plus 3 close paren squared plus open paren y plus 5 close paren squared is equal to 6
C
open paren x minus 3 close paren squared plus open paren y minus 5 close paren squared is equal to 36
D
open paren x minus 3 close paren squared plus open paren y minus 5 close paren squared is equal to 6
13

A sprinkler is designed to water a circular area that has a radius of 7 feet. The sprinkler is located at 0 comma 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.

A
Yes. The flowerbed is square root of 45 feet away from the sprinkler, which is less than the 7 -foot radius.
B
No. The flowerbed is 18 feet away from the sprinkler, which is more than the 7 -foot radius.
C
No. The flowerbed is 9 feet away from the sprinkler, which is more than the 7 -foot radius.
D
Yes. The flowerbed is exactly 7 feet away from the sprinkler.
14

Which equation represents a circle with a center at negative 4 comma 9 and a diameter of 10 units?

A
open paren x plus 4 close paren squared plus open paren y minus 9 close paren squared is equal to 100
B
open paren x plus 4 close paren squared plus open paren y minus 9 close paren squared is equal to 25
C
open paren x minus 9 close paren squared plus open paren y plus 4 close paren squared is equal to 25
D
open paren x minus 9 close paren squared plus open paren y plus 4 close paren squared is equal to 100
17

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

A
x squared plus open paren y plus 8 close paren squared is equal to 36
B
x squared plus open paren y minus 5 close paren squared is equal to 6
C
open paren x plus 6 close paren squared plus y squared is equal to 144
D
x squared plus open paren y minus 3 close paren squared is equal to 36
E
open paren x minus 4 close paren squared plus y squared is equal to 36
18

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

A
x squared plus open paren y plus 8 close paren squared is equal to 36
B
open paren x plus 6 close paren squared plus y squared is equal to 144
C
x squared plus open paren y minus 5 close paren squared is equal to 6
D
open paren x minus 4 close paren squared plus y squared is equal to 36
E
x squared plus open paren y minus 3 close paren squared is equal to 36

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