Find the Center and Radius x^2+y^2-2x=0

Substitute ${\displaystyle {(x-1)}^2-1}$ for ${\displaystyle x^2-2x}$ in the equation ${\displaystyle x^2+y^2-2x=0}$.

Move ${\displaystyle -1}$ to the right side of the equation by adding ${\displaystyle 1}$ to both sides.

Add ${\displaystyle 0}$ and ${\displaystyle 1}$.

This is the form of a circle. Use this form to determine the center and radius of the circle.

Match the values in this circle to those of the standard form. The variable ${\displaystyle r}$ represents the radius of the circle, ${\displaystyle h}$ represents the x-offset from the origin, and ${\displaystyle k}$ represents the y-offset from origin.

The center of the circle is found at ${\displaystyle (h,k)}$.

Center: ${\displaystyle (1,0)}$

These values represent the important values for graphing and analyzing a circle.

Center: ${\displaystyle (1,0)}$

Radius: ${\displaystyle 1}$