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If t is the parameter for one end of a focal chord of the parabola y 2   = 4 a x , then its length is

Options

  1. Aa t + 1 t 2
  2. Ba t - 1 t 2
  3. Ca t + 1 t
  4. Da t - 1 t

Correct answer

A. a t + 1 t 2

Step-by-step solution

For a focal chord of parabola t 1 t 2 = - 1 ,where t 1 and t 2 are parameters of two ends of the focal chord. Since one end is given t , then value of the parameter for the other end of the focal chord is = - 1 t ∴   The co-ordinates of the end points of the focal chords are a t 2 ,   2 a t and a t 2 , - 2 a t ∴   Length of the focal chord = a t 2 - a t 2 2 + 2 a t + 2 a t 2 = a t 4 + 1 t 4 - 2 + 4 t 2 + 4 t 2 + 8 = a t 4 + 1 t 4 + 4 t 2 + 4 t 2 + 6 = a t 2 + 1 t 2 + 2 2 = a t 2 + 1 t 2 +

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