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Question

Let PQ be a focal chord of y2=4ax. The tangents to parabola at P and Q meet at a point lying on the line y=2x+a (a>0). Length of PQ(in units) is :

A
7a
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B
5a
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C
3a
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D
2a
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Solution

The correct option is B 5a
Let point of intersection of tangents at extremeties of focal chord be R=(at1t2,a(t1+t2)),t1t2=1
R lies on the directix x=a and it also lies on line y=2x+a
y=a=a(t1+t2)
t1+t2=1
(t2t1)2=(t1+t2)24t1t2=5
PQ=(a(t21t22))2+(2a(t1t2))2
PQ=(a(t1+t2)(t1t2))2+(2a(t1t2))2
Putting values, we get PQ=5a

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