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Condition For Perpendicularity

A ray of ligh...

Question

A ray of light is coming along the line which is parallel to y-axis and strikes a concave mirror whose intersection with the XY-plane is a parabola ${(x - 4)}^{2} = 4 (y + 1)$ .
After reflection, the ray must pass through the point?

(4, - 1)

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(0, 1)

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(- 4, 1)

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None of these

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Solution

The correct option is C $(4, - 1)$
The equation of axis of the parabola is $x - 4 = 0$ which is parallel to y-axis.
So, the ray of light is parallel to the axis of the parabola.
We know that nay ray parallel to the axis of a parabola passes through the focus after reflection. $∴$ The ray through the point $(4, - 1)$

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