AnswersEHS New Credit Topics in GeometryFigures in the Coordinate Plane (Sec 9-1)

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 (–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
3

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
4

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)
5

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

Question illustration
A
(2, )
Option A
B
(2, )
Option B
C
(2, 1)
D
(2, 3)
8

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.

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

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)
10

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)

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