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Question

The condition that the parabolas y2 = 4c (x – d) and y2 = 4ax have a common normal other then x-axis (a greater than 0, c greater than 0) is

  1. 2a less than 2c + d    
  2. 2c less than 2a + d    
  3. 2d less than 2a + c    
  4. 2d less than 2c + a    

The correct answer is: 2a less than 2c + d


    N1: y = mx –2 am – am3
    [Normal of parabola open y squared equals space 4 a x close square brackets
    N2: y = m(x – d) – 2cm – cm3
    [Normal of parabola y squared equals 4 c left parenthesis x minus d right parenthesis]
    On comparing both equations – 2am – am3 = – md – 2cm – am3 for two distinct root D greater than 0.

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