Explanation

(c)
Centre and radius of the given circle are (1, 0)and 1.
Let the centre of the image circle be ($x_{1}$,$y_{1}$)
Hence, $(x_{1},\ y_{1})$ be the image of the point (1, 0)
w.r.t. the line $x + y = 2$, then
$\frac{x_{1} - 1}{1} = \frac{y_{1} - 0}{1} = \frac{- 2\lbrack 1(1) + 1(0) - 2\rbrack}{(1)^{2} + (1)^{2}}$
$\Rightarrow \ \ \ \frac{x_{1} - 1}{1} = \frac{y_{1}}{1} = 1$
$\Rightarrow \ \ x_{1} = 2,\ y_{1} = 1$
$\therefore$ Equation of the imaged circle is
$(x - 2)^{2} + (y - 1)^{2} = 1^{2}$
$\Rightarrow x^{2} + y^{2} - 4x - 2y + 4 = 0$