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# Common Core Standard HSG-GPE.A.1 Questions

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

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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. $(x-2)^2+(y-5)^2=25$
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. $(x+2)^2+(y-2)^2=4$
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. $(x+2)^2+(y+2)^2=149$
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. $(x-1)^2+(y+4)^2=289$