Equation of a Circle — Quiz Answers

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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
open paren x minus 4 close paren squared plus y squared is equal to 10
B
x squared plus open paren y minus 4 close paren squared is equal to 100
C
x squared plus open paren y minus 4 close paren squared is equal to 10
D
open paren x minus 4 close paren squared plus y squared is equal to 100
23

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
open paren x minus 4 close paren squared plus y squared is equal to 10
B
x squared plus open paren y minus 4 close paren squared is equal to 10
C
x squared plus open paren y minus 4 close paren squared is equal to 100
D
open paren x minus 4 close paren squared plus y squared is equal to 100
24

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 square root of the constant term, z .
B
The radius is the constant term, z , divided by 2 .
C
The radius is the square of the constant term, z .
D
The radius is the constant term, z .
25

Does the point 1 comma square root of 7 lie on the circle shown? Explain.

A
No, the distance from negative 2 comma 0 to 1 comma square root of 7 is not 4 units.
B
Yes, the distance from negative 2 comma 0 to 1 comma square root of 7 is 4 units.
C
Yes, the distance from negative 2 comma 4 to 1 comma square root of 7 is 4 units.
D
No, the distance from negative 2 comma 4 to 1 comma square root of 7 is not 4 units.
27

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 minus 1 close paren squared plus open paren y plus 2 close paren squared is equal to 5
B
open paren x plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 5
C
open paren x minus 1 close paren squared plus open paren y plus 2 close paren squared is equal to 25
D
open paren x plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 25
28

Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?

A
open paren x minus 5 close paren squared plus open paren y minus 4 close paren squared is equal to 2
B
open paren x minus 5 close paren squared plus open paren y minus 4 close paren squared is equal to 4
C
open paren x minus 4 close paren squared plus open paren y minus 5 close paren squared is equal to 4
D
open paren x minus 4 close paren squared plus open paren y minus 5 close paren squared is equal to 2
29

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 minus 1 close paren squared plus open paren y plus 2 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 plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 25
D
open paren x plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 5
31

Which equation represents a circle with the same radius as the circle shown but with a center at negative 1 comma 1 ?

A
open paren x minus 1 close paren squared plus open paren y plus 1 close paren squared is equal to 16
B
open paren x plus 1 close paren squared plus open paren y minus 1 close paren squared is equal to 16
C
open paren x minus 1 close paren squared plus open paren y plus 1 close paren squared is equal to 4
D
open paren x plus 1 close paren squared plus open paren y minus 1 close paren squared is equal to 4
33

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 6
B
open paren x plus 3 close paren squared plus open paren y plus 5 close paren squared is equal to 36
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 minus 3 close paren squared plus open paren y minus 5 close paren squared is equal to 36
34

Does the point 2 comma square root of 6 lie on the circle shown? Explain.

A
Yes, the distance from 3 comma 0 to 0 comma 0 is 3 units.
B
Yes, the distance from 0 comma 0 to 2 comma square root of 6 is 3 units.
C
No, the distance from 0 comma 0 to 2 comma square root of 6 is not 3 units.
D
No, the distance from 3 comma 0 to 2 comma square root of 6 is not 3 units.
37

Which completes the work correctly?

A
open paren x minus 3 close paren squared plus open paren y minus 2 close paren squared is equal to 4 squared , so the center is negative 3 comma negative 2 .
B
open paren x plus 3 close paren squared plus open paren y plus 2 close paren squared is equal to 4 squared , so the center is 3 comma 2 .
C
open paren x minus 3 close paren squared plus open paren y minus 2 close paren squared is equal to 4 squared , so the center is 3 comma 2 .
D
open paren x plus 3 close paren squared plus open paren y plus 2 close paren squared is equal to 4 squared , so the center is negative 3 comma negative 2 .
38

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 of the constant term, z .
D
The radius is the square root of the constant term, z .
39

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 minus 9 close paren squared plus open paren y plus 4 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 100
D
open paren x plus 4 close paren squared plus open paren y minus 9 close paren squared is equal to 25
40

If the center of the circle were moved from the origin to the point h comma k and point P at x comma y remains on the edge of the circle, which could represent the equation of the new circle?

A
open paren h plus x close paren squared plus open paren k plus y close paren squared is equal to r squared
B
open paren x minus k close paren squared plus open paren y minus h close paren squared is equal to r squared
C
open paren k plus x close paren squared plus open paren h plus y close paren squared is equal to r squared
D
open paren x minus h close paren squared plus open paren y minus k close paren squared is equal to r squared

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