To find the center of the circle from the given equation:

Step 1: Rewrite the equation

The given equation is:

$x^2 + y^2 - 2x = 0$

Reorganize the terms involving $x$:

$x^2 - 2x + y^2 = 0$

Step 2: Complete the square for $x$

To complete the square for $x^2 - 2x$, take half the coefficient of $x$ (which is $-2$), square it, and add it to both sides of the equation.

$\left(\frac{-2}{2}\right)^2 = 1$

Add $1$ to both sides:

$x^2 - 2x + 1 + y^2 = 1$

Step 3: Rewrite the equation

The equation now becomes:

$(x - 1)^2 + y^2 = 1$

Step 4: Identify the center

The equation of a circle is generally written as:

$(x - h)^2 + (y - k)^2 = r^2$

Here, the center of the circle is $(h, k)$. Comparing:

$(x - 1)^2 + (y - 0)^2 = 1$

The center is:

$(1, 0)$

Final Answer:

The center of the circle is $(1, 0)$.

---

Would you like details or further assistance? Here are 5 related questions:

1. How do you determine the radius of the circle from the same equation?
2. What is the general form of the equation of a circle?
3. Can you solve for the center if there are additional terms involving $y$?
4. What does completing the square mean in the context of other conic sections?
5. How would you graph this circle using its equation?

Tip: Always rearrange equations to match the standard form of the circle equation to easily identify the center and radius.