Answers KS-Geometry B-CRUnit Test

Equation of a Circle Answers

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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)

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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

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

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.

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).

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

(2, )

(2, 1)

(2, 3)

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

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.

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.

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Equation of a Circle Answers

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