AnswersSS Integrated Math IIB 2026Parabolas (Sec 9-4)

Equation of a Circle Answers

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1
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Which equation represents a circle that contains the point (–5, –3) and has a center at (–2, 1)? Distance formula:

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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
2
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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.
3

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
4

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
5

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
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.

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.
7

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
A
(h + x)2 + (k + y)2 = r2
B
(x – h)2 + (y – k)2 = r2
C
(k + x)2 + (h + y)2 = r2
D
(x – k)2 + (y – h)2 = r2
8

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
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 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

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