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KVPY2016MathematicsParabola

Suppose the parabola ( y - k )²=4( x - h ) , with vertex A , passes through O =(0,0) and L =(0,2) . Let D be an end point of the latus rectum. Let the y-axis intersect the axis of the parabola at P . Then PDA is equal to

Options

  1. A⁻¹ 1 19
  2. B⁻¹ 2 19
  3. C⁻¹ 4 19
  4. D⁻¹ 8 19

Correct answer

B. ⁻¹ 2 19

Step-by-step solution

Curve, S:(y-k)²=4(x-h) LLR =4 ; Clearly k =1 ; A ( h , 1) & ' M ^ is focus ( h +1,1) So D ( h +1,3) S _ (0,0) =0 k ²=-4 ~h h = -1 4 D ( 3 4 , 3 ) Now ; = | m₁-m₂ 1+m₁ m₂ |= | 8 3 -2 1+ 8 3 2 |= 2 19 where, m₁= 3-1 3 4 -0 = 2 3 4 = 8 3 m ₂= 3-1 1 =2

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