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JEE Advanced2013MathematicsParabolaActual

Paragraph: Let P Q be a focal chord of the parabola y²=4 a x . The tangents to the parabola at P and Q meet at a point lying on the line y=2 x+a, a>0 . Question: Length of chord P Q is

Options

  1. A7 a
  2. B5 a
  3. C2 a
  4. D3 a

Correct answer

B. 5 a

Step-by-step solution

R lies on y = 2x + a R ,   y   =   2 x   +   a ⇒ a  t - 1 t = - a t - 1 t = - 1 ⇒ t + 1 t 2 = 1 + 4 = 5 PQ = a  t + 1 t 2 = 5 a

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