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Question

The chord AB of the parabola y2=4ax cuts the axis of the parabola at C. If
A=(at21,2at1),B=(at22,2at2) and AC:AB=1:3, then :

A
t2=2t1
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B
t2+2t1=0
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C
t1+2t2=0
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D
None of these
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Solution

The correct option is A t2=2t1
Equation of chord AB is y(t1+t2)2x+2at1t2
Since it cuts axis of parabola at C
coordinate of C are (at1,t2,0)
Now AC:AB=1:3
1.2at26at113=0t22t1=0t2=2t1

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