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Question
Let P and Q be the points on the parabola y2=4x so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
Let P and Q be the points on the parabola y2=4x so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
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Solution
The correct option is B 4
According to question, it is given that slope of PX and QX are perpendicular to each other, i.e., slope of PX× slope of XQ=−1
⇒2tt2×2mm2=−1
⇒tm=−4
PQ:x−t2t2−m2=y−2t2t−2m
Let PQ meets axis of parabola i.e., x-axis at R(α,0), then
α−t2(t+m)(t−m)=0−2t2(t−m)
⇒α−t2=−t2−tm=−t2+4
⇒α=4⇒AR=4
According to question, it is given that slope of PX and QX are perpendicular to each other, i.e., slope of PX× slope of XQ=−1
⇒2tt2×2mm2=−1
⇒tm=−4
PQ:x−t2t2−m2=y−2t2t−2m
Let PQ meets axis of parabola i.e., x-axis at R(α,0), then
α−t2(t+m)(t−m)=0−2t2(t−m)
α−t2(t+m)(t−m)=0−2t2(t−m)
⇒α−t2=−t2−tm=−t2+4
⇒α=4⇒AR=4
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