Equations of a Circle

The Equation of a Circle

Writing Equations and Graphing Circles

Multiple Choice

Which is the correct equation of a circle that is centered at the origin (0,0) and has a radius of 2?

• x² + y² = 2

• x² + y² = 3

• x² + y² = 4

• (x - 2)² + (y - 2)² = 4

Multiple Choice

Which equation matches the circle on the graph?

• x²+y²=16

• x²+y²=32

• 2x²+5y²=256

• 24x²+999y²=16

Multiple Choice

Write the equation at the origin with radius 6.  

• x^2 + y^2 = 6
• x^2 + y^2 = 36
• x  + y = 6
• x + y = 36

Multiple Choice

What does the equation of a circle with center at (0,0) look like?

• $y=x^2$

• $y=mx+b$

• $x^2+y^2=r^2$

• $y=a\left(x-h\right)^2+k$

Multiple Choice

What is the center of the circle with equation x² + y² = 1?

• (1, 1)
• (0, 0)
• not enough information

Multiple Choice

What is the radius of the circle with equation x² + y² = 1?

• 0
• 0.5
• 1
• 2

Multiple Choice

What is the equation for this circle?

• (x+1)²+(y+1)²=9

• x²+y²=9

• x²+y²=6

• x²+y²=3

Multiple Choice

What does the r in the standard equation stand for?

• r is the distance of the circle

• r is the radius of the circle

• r is the x coordinate of the center of the circle

• r is the y coordinate of the center of the circle

Multiple Choice

Which equation matches the circle on the graph?

• (x+2)²+y²=16

• (x+2)²+x²=16

• (x+4)²+y²=4

• (x+20)²+y²=12

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9
• x² + (y -7)² = 9
• (x - 7)² + y² = 3
• x² + (y -7)² = 3

Multiple Choice

What does "h" stand for in (h,k)?

• h is the radius of the circle

• h is the distance of the circle

• h is the y coordinate of the center

• h is the x coordinate of the center

Multiple Choice

Which of the following is the center of the circle?

(x + 8)² + y² = 16

• (8,0)

• (-8,0)

• (0,8)

• (0,-8)

Multiple Choice

Which is the correct graph for (x+2)² + y² = 9?

Multiple Choice

What is the equation of a circle with radius 4 and center (0, 8)?

• x² + (y-8)² = 16
• (x-8)² + y² = 4
• x² + (y-8)² = 4
• x² + (y+8)² = 16

Multiple Choice

What is the equation of circle with a center of (0, -3) and a diameter of 8

• x² + (y+3)² = 16

• x² + (y-3)² = 16

• x² + (y+3)² = 64

• x² + (y-3)² = 64

Multiple Choice

What is the equation for the circle graphed?

• $x^2+y^2=4$

• $x^2+\left(y-2\right)^2=2$

• $x^2+\left(y-2\right)^2=4$

• $\left(x-2\right)^2+y^2=4$

Multiple Choice

What does the "k" in (h,k) stand for?

• k is the y coordinate of the center

• k is the x coordinate of the center

• k is the radius of the circle

• k is the distance of the circle

Multiple Choice

Which is the correct equation for the graph given?

• (x -1)² + y² = 4

• (x +1)² + y² = 4

• x ² + (y-1)² = 4

• x ² + (y+1)² = 4

Multiple Choice

Which graph correctly graphs

x ² + (y+4)² = 1?

Multiple Choice

What is the correct equation of the given circle in general form?

• A

• B

• C

• D

Multiple Choice

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4
• 2
• 3
• 16

Multiple Choice

What is the equation of the circle, with center (4,2) and radius 5 units?

• (x + 4)² + (y + 2)² = 25
• (x + 4)² + (y + 2)² = 5
• (x - 4)² + (y - 2)² = 5
• (x - 4)² + (y - 2)² = 25

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)
• (-3, -2)
• (-2, -3)
• (2, 3)

Multiple Choice

What is the radius of the circle given by the equation (x-7)² + (y+3)² = 25?

• 3
• 5
• 10
• 25

Multiple Choice

In the equation
(x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)
• (-3, -2)
• (-2, -3)
• (2, 3)

Multiple Choice

See Picture

• A
• B
• C
• D

Multiple Choice

What is the equation of the circle?

• (x+1)^2 + (y +1)^2 = 3

• (x+1)^2 + (y -1)^2 = 3

• (x+1)^2 + (y +1)^2 = 9

• (x-1)^2 + (y -1)^2 = 9

Multiple Choice

What is the center and radius for a circle with the equation:
(x-4)²+(y+2)²=25

• C:(4, -2), r=5
• C:(-4, 2), r=5
• C:(4, -2), r=25
• C:(-4, 2), r=25

Multiple Choice

Which graph corresponds to 
(x)²+ (y-6)²=9

• A
• B
• C
• D

Multiple Choice

What is the equation of a circle with a center of (9, -2) and a diameter of 12

• (x-9)² + (y+2)² = 144

• (x+9)² + (y-2)² = 36

• (x-9)² + (y+2)² = 36

• (x+9)² + (y-2)² = 144

Multiple Choice

What is the radius of the circle given by the equation (x - 7)² + (y + 3)² = 25?

• 3

• 5

• 10

• 25

Multiple Choice

What is the radius of the circle given by the equation (x - 7)² + (y + 3)² = 25?

• 3

• 5

• 10

• 25