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(C) The equation of the parabola is $y^2 - 2y - 4x + 5 = 0$.Completing the square for $y$,we get $(y-1)^2 - 1 - 4x + 5 = 0$,which simplifies to $(y-1)

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$y = -1$

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(C) The equation of the parabola is $y^2 - 2y - 4x + 5 = 0$.Completing the square for $y$,we get $(y-1)^2 - 1 - 4x + 5 = 0$,which simplifies to $(y-1)^2 = 4x - 4$,or $(y-1)^2 = 4(x-1)$.This is a parabola with vertex $V(1, 1)$ and focus $F(1+1, 1) = (2, 1)$.The incident ray travels along the line $x = 2$,which is the line passing through the focus $F(2, 1)$ and parallel to the $y$-axis.According to the reflective property of a parabola,any ray of light parallel to the axis of the parabola and striking the mirror will pass through the focus after reflection,and conversely,any ray passing through the focus will be reflected parallel to the axis of the parabola.The axis of this parabola is the line $y = 1$.Since the incident ray passes through the focus $F(2, 1)$,the reflected ray must be parallel to the axis of the parabola,which is $y = 1$.Thus,the reflected ray is a horizontal line of the form $y = k$.From the provided image,the reflected rays are $y = 3$ and $y = -1$. Comparing this with the options,$y = -1$ is a valid reflected ray.

$A$ ray of light travelling along the line $x = 2$ strikes a parabolic mirror with the equation $y^2 - 2y - 4x + 5 = 0$ and gets reflected from its surface. Then,the equation of the reflected ray may be:

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