Equation of a Circle

Question 1

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.

Revolt · Accepted Answer

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

Question 2

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

Revolt · Accepted Answer

(x – 4)2 + y2 = 100

Question 3

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

Revolt · Accepted Answer

(x + 1)2 + (y – 1)2 = 16

Question 4

Distance formula:

Revolt · Accepted Answer

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

Question 5

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

Revolt · Accepted Answer

(x + 4)2 + (y – 9)2 = 25

Question 6

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

Revolt · Accepted Answer

(2, )

Question 7

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

Revolt · Accepted Answer

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

Question 8

Distance formula:

Revolt · Accepted Answer

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

Question 9

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

Revolt · Accepted Answer

(–2, 4)

Question 10

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

Revolt · Accepted Answer

(x – 4)2 + (y – 5)2 = 4

Equation of a Circle Answers

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