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Question

The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is c. Then

  1. 2a2 = bc    
  2. a3 = b2c    
  3. ac = b2    
  4. b2c = 4a3    

The correct answer is: b2c = 4a3


    Chord joining two points t1 and t2 is
    (t1 + t2)y = 2x + 2at1t2
    open vertical bar fraction numerator 2 a t subscript 1 end subscript t subscript 2 end subscript over denominator square root of 4 plus left parenthesis t subscript 1 end subscript plus t subscript 2 end subscript right parenthesis to the power of 2 end exponent end root end fraction close vertical bar= b... (1)
    a (t1 – t2)2 = c ... (2)
    By using (1) and (2), eliminate t1 & t2

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