Answers EBR - Geometry B-CR SUMMER 2026Equation of a Circle

Equation of a Circle Answers

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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

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

(–2, 4)

(–4, 8)

(2, –4)

(4, –8)

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

(2, )

(2, )

(2, 1)

(2, 3)

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

2 units

3 units

4 units

5 units

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)

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.

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 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 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

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 = 36x2 + (y – 5)2 = 6(x – 4)² + y² = 36(x + 6)² + y² = 144x2 + (y + 8)2 = 36

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

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

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.

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Equation of a Circle Answers

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