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Question

If an incident ray from the point (−1,2) parallel to the axis of the parabola
y2=4x strikes the parabola, then what is the equation of the reflected ray?

A
3x=2
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B
2x+3=0
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C
x=1
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D
x=1
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Solution

The correct option is C x=1
The incident ray is parallel to the x-axis, so the y-coordinate of the point will be the same as the y-coordinate of the point in the parabola at which the ray strikes.
On putting the y-coordinate as 2 in y2=4x, we get the x-coordinate of the point at which the ray strikes.

Therefore, the incident ray from (1,2) strikes the parabola at P(1,2).

Also, the reflected rays pass through the focus.


The focus of this parabola is (1,0).

So the equation of the reflected ray is the equation of the straight line joining the points P and the focus.

Hence, the equation of the reflected ray is
x=1.

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