Explanation

(c)
Any point on the given parabola is $(t^{2},\ 2t)$. The equation of the tangent at $(1,\ 2)$ is $x - y + 1 = 0$
The image $(h,\ k)$ of the point $(t^{2},\ 2t)$ in $x - y + 1 = 0$ is given by $\frac{h - t^{2}}{1} = \frac{k - 2t}{- 1} = \frac{- 2(t^{2} - 2t + 1)}{1 + 1}$
$\therefore h = t^{2} - t^{2} + 2t - 1 = 2t - 1$
And $k = 2t + t^{2} - 2t + 1 = t^{2} + 1$
On eliminating $t$ from $h = 2t - 1$ and $k = t^{2} + 1$
We get, ${(h + 1)}^{2} = 4(k - 1)$
The required equation of reflection is
${(x + 1)}^{2} = 4(y - 1)$