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The graph of x^2 - 2x + y^2 = 24 is a circle. Find the center and radius of this circle.

 Jun 30, 2022
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Add 1 to complete the square on x: \(x^2-2x +1 + y^2 = 25\)

 

Complete the square: \((x-1)^2 + y^2 = 25\)

 

The center occurs at \(\color{brown}\boxed{(1,0)}\), (x-y pair when the value of the circle equals 0). 

 

Also, note that the constant on the right-hand side of the equation equals the radius squared, so the radius is \(\sqrt {25} = \color{brown}\boxed 5\)

 Jun 30, 2022

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