The intercept on the line y = x by the circle x2+y2−2x=0 is AB. The equation of the circle with AB as diameter, is

The equation of the circle passing through the intersect-ion of the circle x2+y2−2x=0 and the line (AB whose equation is y = x), is x2+y2−2x+λ(y−x)=0⇒x2+y2−x(2+λ)+λy=0Line y = x will be a diameter of this circle, if it passes throughthe centre 2+λ2,−λ2∴ −λ2=2+λ2⇒λ=−1.Putting λ=−1 in (i)  we getx2+y2−x−y=0 as the equation of the required circle