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 At2=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 ⇒1.2at2−6at11−3=0⇒t2−2t1=0⇒t2=2t1