Explanation

(a)
The intersection of given line and circle is
$x^{2} + y^{2} - 2x = 0$
$\Rightarrow \ \ 2x(x - 1) = 0$
$\Rightarrow x = 0,\ x = 1$
And $y = 0,\ 1$
Let coordinates of $A$ are (0, 0) and coordinates of $B$ are (1, 1).
$\therefore$ Equition of circle ($AB$ as a diameter) is
$(x - x_{1})\left( x - x_{2} \right) + \left( y_{-}y_{1} \right)\left( y - y_{2} \right) = 0$
$\Rightarrow \ \ (x - 0)(x - 1) + (y - 0)(y - 1) = 0$
$\Rightarrow x^{2} + y^{2} - x - y = 0$