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JEE Main202621 January 2026Evening ShiftMathematicsParabolaActual

Let one end of a focal chord of the parabola y²=16 x be (16,16) . If P ( , ) divides this focal chord internally in the ratio 5: 2 , then the minimum value of + is equal to :

Options

  1. A16
  2. B5
  3. C7
  4. D22

Correct answer

C. 7

Step-by-step solution

Parabola y^2 = 16x , a = 4 , focus at (4, 0) . Point (16, 16) has parameter t₁ = 2 . Other end of focal chord: t₂ = -1/t₁ = -1/2 , giving (4 1/4, 8 (-1/2)) = (1, -4) . P divides the chord in ratio 5:2 internally (two cases): From (16,16) to (1,-4) : P = ( 37 7 , 12 7 ) , + = 7 . From (1,-4) to (16,16) : P = ( 82 7 , 72 7 ) , + = 22 . Minimum value of + = 7 .

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