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Question

If the point t is one extremity of a focal chord of the parabola y2=4ax then the length of the chord is
  1. a
  2. at


Solution

The correct option is A
If t1 is the other end of the focal chord, then the equation of the chord is y(t+t1)=2x+2att1
Since it passes through the focus (a, 0), we get 2a+2att1=0tt1=1t1=1t
Length of the chord = (at2at21)2+(2at2at1)2=a(t21t2)2+4(t+1t)2
=a(t+1t)(t1t)2+4=a(t+1t)2

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