AnswersMath II CR S2 RS3Equation 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.

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
2
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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
3

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

Question illustration
A
(x – 1)2 + (y + 1)2 = 16
B
(x – 1)2 + (y + 1)2 = 4
C
(x + 1)2 + (y –1)2 = 4
D
(x + 1)2 + (y – 1)2 = 16
4

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.
5

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
6

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

Question illustration
A
(x – 4)2 + y2 = 100
B
(x – 4)2 + y2 = 10
C
x2 + (y – 4)² = 10
D
x2 + (y – 4)² = 100
7

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
8

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

Question illustration
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
9

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

A
(−9,6)
B
(−6,9)
C
(6,−9)
D
(9,−6)
10

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

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Equation of a Circle Answers — Math II CR S2 RS3