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# Coordinates

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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