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JEE Advanced2017MathematicsParabolaActual

If a chord, which is not a tangent, of the parabola y 2 = 16 x has the equation 2 x + y = p , and midpoint (h, k), then which of the following is (are) possible value(s) of p , h and k ?

Options

  1. Ap = - 2 , h = 2 , k = - 4
  2. Bp = 5 , h = 4 , k = - 3
  3. Cp = - 1 , h = 1 , k = - 3
  4. Dp = 2 , h = 3 , k = - 4

Correct answer

D. p = 2 , h = 3 , k = - 4

Step-by-step solution

Equation of chord with mid point ( h ,   k ) : k . y - 16 x + h 2 = k 2 - 16 h ⇒ 8 x - k y + k 2 - 8 h = 0   Comparing with 2 x + y - p = 0 , we get k = - 4 ; 2 h - p = 4 Only p = 2 ,   h = 3 ,   k = - 4 satisfies above relation.

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