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Equations of Circles (Grades 11-12)

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Equations of Circles

1. 
Identify the center and the radius: [math] (x - 6)^2 + (y - 4)^2 = 9.[/math]
  1. Center (6, 4), radius 9
  2. Center (-6, -4), radius 3
  3. Center (6, 4), radius 3
2. 
Find the center and radius of: [math](x-2/3)^2+(y+1/2)^2=9/4.[/math]
  1. Center [math](-2/3, -1/2), \ [/math] Radius of [math]3/2[/math]
  2. Center [math](2/3, -1/2), \ [/math] Radius of [math]3/2[/math]
  3. Center [math](2/3, -1/2), \ [/math] Radius of [math]9/4[/math]
  4. Center [math](-2/3, 1/2), \ [/math] Radius of [math]9/4[/math]
3. 
What is the equation of a circle with a center of (0, 0) and a radius of 5?
  1. [math]x^2-y^2=25[/math]
  2. [math]x^2+y^2=25[/math]
  3. [math]x^2+y^2=5[/math]
  4. [math]x^2-y^2=5[/math]
4. 
What is the equation for a circle with center [math](-2,-2)[/math] and the outer point of the radius at [math](7,10)[/math]?
  1. [math](x-2)^2+(y-2)^2=100[/math]
  2. [math](x+2)^2+(y+2)^2=225[/math]
  3. [math](x-2)^2+(y-2)^2=289[/math]
  4. [math](x+2)^2+(y+2)^2=149[/math]
5. 
A circle with equation [math](x+4)^2 + (y-3)^2 = 16[/math] is shifted 5 units to the right. What is the equation of the new circle?
  1. [math](x-1)^2+ (y - 3)^2 = 16[/math]
  2. [math](x+1)^2+ (y + 3)^2 = 16[/math]
  3. [math](x-1)^2+ (y - 8)^2 = 16[/math]
  4. [math](x-5)^2+ (y - 5)^2 = 16[/math]
6. 
Given the equation of a circle [math] (x - 5)^2 + (y + 1)^2 = 9[/math], what is the sum of the x-coordinate of the center, the y-coordinate of the center, and the radius of the circle?
  1. 13
  2. 7
  3. 5
  4. -1
7. 
Find the center and radius of the circle with the equation [math](x-1)^2+y^2=16[/math].
  1. (1,0); 4
  2. (-1,0); 16
  3. (0,1); 4
  4. (0,-1); 16
8. 
Write an equation for a circle if the endpoints of a diameter are at (1,1) and (1,-9).
  1. [math](x-1)^2+(y+4)^2=5[/math]
  2. [math](x-1)^2+(y+4)^2=25[/math]
  3. [math](x+1)^2+(y-4)^2=5[/math]
  4. [math](x+1)^2+(y-4)^2=25[/math]
9. 
Find the center and radius of the circle with the equation [math](x-2)^2+y^2=9[/math].
  1. (-2,0); 9
  2. (0,2); 9
  3. (2,0); 3
  4. (0,-2); 3
10. 
What is the equation for a circle with center [math](-4,6)[/math] and radius of 6?
  1. [math](x+4)^2+(y-6)^2=12[/math]
  2. [math](x-4)^2+(y+6)^2=36[/math]
  3. [math](x+4)^2+(y+6)^2=12[/math]
  4. [math](x+4)^2+(y-6)^2=36[/math]
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