Answers CR CCSS Math 2 S2 M2960OXPerformance Task: Circle Constructions

Lesson 10.9: Equation of a Circle Answers

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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.

No. The flowerbed is 18 feet away from the sprinkler, which is more than the 7-foot radius.

Yes. The flowerbed is exactly 7 feet away from the sprinkler.

No. The flowerbed is 9 feet away from the sprinkler, which is more than the 7-foot radius.

Yes. The flowerbed is √45 feet away from the sprinkler, which is less than the 7-foot radius.

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

(x – 4)2 + y2 = 100

(x – 4)2 + y2 = 10

x2 + (y – 4)² = 10

x2 + (y – 4)² = 100

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

(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

Distance formula:

Yes, the distance from (–2, 4) to (1, ) is 4 units.

Yes, the distance from (–2, 0) to (1, ) is 4 units.

No, the distance from (–2, 0) to (1, ) is not 4 units.

No, the distance from (–2, 4) to (1, ) is not 4 units.

Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units?

(x – 9)2 + (y + 4)2 = 25

(x + 4)2 + (y – 9)2 = 25

(x – 9)2 + (y + 4)2 = 100

(x + 4)2 + (y – 9)2 = 100

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

(2, )

(2, 1)

(2, 3)

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

The radius is the constant term, z.

The radius is the constant term, z, divided by 2.

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

The radius is the square of the constant term, z.

Distance formula:

Yes, the distance from (3, 0) to (0, 0) is 3 units.

Yes, the distance from (0, 0) to (2, ) is 3 units.

No, the distance from (3, 0) to (2, ) is not 3 units.

No, the distance from (0, 0) to (2, ) is not 3 units.

What is the center of a circle whose equation is x2 + y2 + 4x – 8y + 11 = 0?

(–2, 4)

(–4, 8)

(2, –4)

(4, –8)

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

(x – 4)2 + (y – 5)2 = 2

(x – 4)2 + (y – 5)2 = 4

(x – 5)2 + (y – 4)2 = 2

(x – 5)2 + (y – 4)2 = 4

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).

Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?

(x – 3)2 + (y – 5)2 = 6

(x – 3)2 + (y – 5)2 = 36

(x + 3)2 + (y + 5)2 = 6

(x + 3)2 + (y + 5)2 = 36

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.

(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

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

(–12, –2)

(–6, –1)

(6, 1)

(12, 2)

What is the center of a circle represented by the equation (x+9)2+(y−6)2=102?

(−9,6)

(−6,9)

(6,−9)

(9,−6)

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

2 units

3 units

4 units

5 units

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 = 36

x2 + (y – 5)2 = 6

(x – 4)² + y² = 36

(x + 6)² + y² = 144

x2 + (y + 8)2 = 36

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

(x – 1)2 + (y + 2)2 = 25

(x + 2)2 + (y – 1)2 = 5

(x + 2)2 + (y – 1)2 = 25

(x – 1)2 + (y + 2)2 = 5