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

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

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Solution:

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 any ray parallel to the axis of a parabola passes through the focus after reflection.
$\therefore $The ray must pass through the point $(4,-1)$.