Final answer:
The circle given by the equation x² + y² - 2x = 0 has a centre at (1, 0) and a radius of 1. This is determined by completing the square on the x-terms and then rewriting the equation in the standard form of a circle.
Step-by-step explanation:
To find the radius and centre of the circle given by the equation x² + y² - 2x = 0, we start by completing the square for the x-terms. First, add the square of half the coefficient of x to both sides of the equation, which in this case is (2/2)² = 1. So the equation becomes:
x² - 2x + 1 + y² = 1
Rewrite the equation as:
(x - 1)² + y² = 1²
This represents a circle with a centre at (1, 0) and a radius of 1. The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the centre and r is the radius.