How to Find Equation of a Circle? (+FREE Worksheet!)

Find the equation of a circle from its center and radius.

The equation of a circle with center (h, k) and radius r is (x minus h) squared plus (y minus k) squared equals r squared. If the equation is not in that form, completing the square on both variables gets it there.

Exercises for the Equation of a Circle

Write the standard form equation of each circle.

1. (color{blue}{x^2+y^2-2x+2y=7})
2. (color{blue}{x^2+y^2+12x+8y=-3})
3. (color{blue}{x^2+y^2+8x-2y=8})
4. (color{blue}{x^2+y^2-4x-8y-4=0})
5. (color{blue}{Center: (2,-4), Radius: 5})
6. (color{blue}{Center: (-1,-5), Area: 16π})

1. (color{blue}{(x-1)^2+(y-(-1))^2=3^2})
2. (color{blue}{(x-(-6))^2+(y-(-4))^2=7^2})
3. (color{blue}{(x-(-4))^2+(y-1)^2=5^2})
4. (color{blue}{(x-2)^2+(y-4)^2=(2sqrt{6})^2})
5. (color{blue}{(x-2)^2+(y-(-4))^2=5^2})
6. (color{blue}{(x-(-1))^2+(y-(-5))^2=4^2})

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