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# Equations of Circles - Practice #2

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## Equations of Circles - Practice #2 Answer Key

1.
Given the equation of a circle, $(x-3)^2+(y+5)^2=10$, what is the circle's radius?
1. $5$
2. $100$
3. $sqrt5$
4. $sqrt10$
2.
What is the equation for a circle with center $(2,5)$ and radius of 5?
1. $(x+2)^2+(y+5)^2=25$
2. $(x-2)^2+(y-5)^2=5$
3. $(x+2)^2+(y+5)^2=5$
4. $(x-2)^2+(y-5)^2=25$
3.
What is the equation for a circle with center $(2,-2)$ and radius of 2?
1. $(x-2)^2+(y+2)^2=4$
2. $(x-2)^2+(y+2)^2=2$
3. $(x+2)^2+(y-2)^2=2$
4. $(x+2)^2+(y-2)^2=4$
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. $x^2 +y^2=20$
2. $x^2+y^2=40$
3. $x^2+y^2=400$
4. $x^2+y^2=4000$
5.
What is the equation for a circle with center $(1,-4)$ and the outer point of the radius at $(-3,-5)$?
1. $(x-1)^2+(y+4)^2=15$
2. $(x+1)^2+(y-4)^2=15$
3. $(x-1)^2+(y+4)^2=17$
4. $(x-1)^2+(y+4)^2=289$
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. $(x-5)^2+ (y + 5)^2 = 5$
2. $(x-5)^2+ (y - 5)^2 = 5$
3. $(x-5)^2+ (y - 5)^2 = 25$
4. $(x-5)^2+ (y + 5)^2 = 25$
7.
Write an equation for the circle with center (2,1) that passes through (2,4).
1. $(x-2)^2+(y-1)^2=9$
2. $(x-2)^2+(y-1)^2=3$
3. $(x+3)^2+(y+1)^2=9$
4. $(x+3)^2+(y+1)^2=3$
8.
What is the center and radius of the circle given by the following equation?
$x^2 + y^2 -2x +10y + 22 = 0$
1. $"Center": (0, 0), \ "radius": sqrt(22)$
2. $"Center": (-2, 10), \ "radius": sqrt(22)$
3. $"Center": (1,-5), \ "radius": 2$
4. $"Center":(1,-5), \ "radius": 4$
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. $(x-1)^2 + (y-2)^2 = 1$
2. $(x+5)^2 + (y-2)^2 = 9$
3. $(x+2)^2 + (y-2)^2 = 9$
4. $(x+3)^2 + y(-1)^2 = 3$
10.
What is the center and radius of the circle given by the following equation?
$x^2 + y^2 - 18x + 6y + 65 = 0$
1. $"Center": (18, -6), \ "Radius": 65$
2. $"Center": (9,-3), \ "Radius": 5$
3. $"Center": (0,0), \ "Radius": sqrt(65)$
4. $"Center": (-9,3), \ "Radius": 25$
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