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JEE Main20199 Apr 2019Morning ShiftMathematicsParabolaActual

If one end of a focal chord of the parabola, y 2 = 16 x is at 1 , 4 , then the length of this focal chord is

Options

  1. A24
  2. B25
  3. C22
  4. D20

Correct answer

B. 25

Step-by-step solution

The given parabola y 2 = 16 x is of the form y 2 = 4 a x , hence a = 4 and the focus of the parabola is a ,   0 = 4 ,   0 . The equation of a line joining the points x 1 ,   y 1 and x 2 ,   y 2 is y - y 1 = y 2 - y 1 x 2 - x 1 x - x 1 . Therefore, equation of chord joining P 1 ,   4 to focus S 4 ,   0 is y - 0 = - 4 3 x - 4 ⇒ 3 y = - 4 x + 16 ⇒ 4 x   + 3 y - 16 = 0 To find the points where this line will cut the parabola put x = y 2 16 from the parabola into the line,

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