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Equations of Circles - Practice #2 (Grades 11-12)

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Equations of Circles - Practice #2

1. 
Given the equation of a circle, [math](x-3)^2+(y+5)^2=10[/math], what is the circle's radius?
  1. [math]5[/math]
  2. [math]100[/math]
  3. [math]sqrt5[/math]
  4. [math]sqrt10[/math]
2. 
What is the equation for a circle with center [math](2,5)[/math] and radius of 5?
  1. [math](x+2)^2+(y+5)^2=25[/math]
  2. [math](x-2)^2+(y-5)^2=5[/math]
  3. [math](x+2)^2+(y+5)^2=5[/math]
  4. [math](x-2)^2+(y-5)^2=25[/math]
3. 
What is the equation for a circle with center [math](2,-2)[/math] and radius of 2?
  1. [math](x-2)^2+(y+2)^2=4[/math]
  2. [math](x-2)^2+(y+2)^2=2[/math]
  3. [math](x+2)^2+(y-2)^2=2[/math]
  4. [math](x+2)^2+(y-2)^2=4[/math]
4. 
Josh's lawn service company offers services within a 20 mile radius of his office. When the service area is represented graphically with the office located at (0, 0), what is the equation that represents the service area?
  1. [math]x^2 +y^2=20[/math]
  2. [math]x^2+y^2=40[/math]
  3. [math]x^2+y^2=400[/math]
  4. [math]x^2+y^2=4000[/math]
5. 
What is the equation for a circle with center [math](1,-4)[/math] and the outer point of the radius at [math](-3,-5)[/math]?
  1. [math](x-1)^2+(y+4)^2=15[/math]
  2. [math](x+1)^2+(y-4)^2=15[/math]
  3. [math](x-1)^2+(y+4)^2=17[/math]
  4. [math](x-1)^2+(y+4)^2=289[/math]
6. 
A circle is tangent to the x-axis at (5,0) and tangent to the y-axis at (0,-5). Determine the equation of this circle.
  1. [math](x-5)^2+ (y + 5)^2 = 5[/math]
  2. [math](x-5)^2+ (y - 5)^2 = 5[/math]
  3. [math](x-5)^2+ (y - 5)^2 = 25[/math]
  4. [math](x-5)^2+ (y + 5)^2 = 25[/math]
7. 
Write an equation for the circle with center (2,1) that passes through (2,4).
  1. [math](x-2)^2+(y-1)^2=9[/math]
  2. [math](x-2)^2+(y-1)^2=3[/math]
  3. [math](x+3)^2+(y+1)^2=9[/math]
  4. [math](x+3)^2+(y+1)^2=3[/math]
8. 
What is the center and radius of the circle given by the following equation?
[math]x^2 + y^2 -2x +10y + 22 = 0 [/math]
  1. [math]"Center": (0, 0), \ "radius": sqrt(22)[/math]
  2. [math]"Center": (-2, 10), \ "radius": sqrt(22)[/math]
  3. [math]"Center": (1,-5), \ "radius": 2[/math]
  4. [math]"Center":(1,-5), \ "radius": 4[/math]
9. 
If the points (1, 2) and (-5, 2) are endpoints of a diameter of a given circle, what is the equation of this circle?
  1. [math] (x-1)^2 + (y-2)^2 = 1 [/math]
  2. [math] (x+5)^2 + (y-2)^2 = 9 [/math]
  3. [math] (x+2)^2 + (y-2)^2 = 9 [/math]
  4. [math] (x+3)^2 + y(-1)^2 = 3 [/math]
10. 
What is the center and radius of the circle given by the following equation?
[math] x^2 + y^2 - 18x + 6y + 65 = 0 [/math]
  1. [math] "Center": (18, -6), \ "Radius": 65 [/math]
  2. [math] "Center": (9,-3), \ "Radius": 5 [/math]
  3. [math] "Center": (0,0), \ "Radius": sqrt(65) [/math]
  4. [math] "Center": (-9,3), \ "Radius": 25 [/math]
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