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# Equations of Circles (Grades 11-12)

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## Equations of Circles

1.
Identify the center and the radius: $(x - 6)^2 + (y - 4)^2 = 9.$
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: $(x-2/3)^2+(y+1/2)^2=9/4.$
1. Center $(-2/3, -1/2), \$ Radius of $3/2$
2. Center $(2/3, -1/2), \$ Radius of $3/2$
3. Center $(2/3, -1/2), \$ Radius of $9/4$
4. Center $(-2/3, 1/2), \$ Radius of $9/4$
3.
What is the equation of a circle with a center of (0, 0) and a radius of 5?
1. $x^2-y^2=25$
2. $x^2+y^2=25$
3. $x^2+y^2=5$
4. $x^2-y^2=5$
4.
What is the equation for a circle with center $(-2,-2)$ and the outer point of the radius at $(7,10)$?
1. $(x-2)^2+(y-2)^2=100$
2. $(x+2)^2+(y+2)^2=225$
3. $(x-2)^2+(y-2)^2=289$
4. $(x+2)^2+(y+2)^2=149$
5.
A circle with equation $(x+4)^2 + (y-3)^2 = 16$ is shifted 5 units to the right. What is the equation of the new circle?
1. $(x-1)^2+ (y - 3)^2 = 16$
2. $(x+1)^2+ (y + 3)^2 = 16$
3. $(x-1)^2+ (y - 8)^2 = 16$
4. $(x-5)^2+ (y - 5)^2 = 16$
6.
Given the equation of a circle $(x - 5)^2 + (y + 1)^2 = 9$, 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 $(x-1)^2+y^2=16$.
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. $(x-1)^2+(y+4)^2=5$
2. $(x-1)^2+(y+4)^2=25$
3. $(x+1)^2+(y-4)^2=5$
4. $(x+1)^2+(y-4)^2=25$
9.
Find the center and radius of the circle with the equation $(x-2)^2+y^2=9$.
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 $(-4,6)$ and radius of 6?
1. $(x+4)^2+(y-6)^2=12$
2. $(x-4)^2+(y+6)^2=36$
3. $(x+4)^2+(y+6)^2=12$
4. $(x+4)^2+(y-6)^2=36$
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