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Question

Let P and Q are the points on the parabola y2=4x, if so that the line segment PQ subtends a right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is


A

1

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B

2

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C

4

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D

6

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Solution

The correct option is C

4


Explanation for the correct option.

Finding the distance of the vertex fromR

It shows in the figure that slope of PX and QX are perpendicular to each other,

so product of slope of both lines will be equal to -1

2tt2×2mm2=-1tm=-4

PQ:x−t2t2-m2=y−2t2t−2mα−t2(t+m)(t-m)=0−2t2(t−m)​⇒α−t2=−t2−tm⇒α=4​[letR(α,0)]

Hence, the correct option is (C)


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