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JEE Main202127 Aug 2021Morning ShiftMathematicsParabolaActual

A tangent and a normal are drawn at the point P ( 2 , - 4 ) on the parabola y 2 = 8 x , which meet the directrix of the parabola at the points A and B respectively. If Q ( a , b ) is a point such that A Q B P is a square, then 2 a + b is equal to

Options

  1. A- 12
  2. B- 20
  3. C- 16
  4. D- 18

Correct answer

C. - 16

Step-by-step solution

Equation of tangent at 2 ,   - 4   T = 0 - 4 y = 4 x + 2 x + y + 2 = 0       . . . ( 1 ) Equation of normal x - y + λ =0 2 ,   - 4 λ = - 6 Thus, x - y = 6         . . . ( 2 ) Equation of normal POI of ( 1 )   &   x = - 2 is A - 2 ,   0 POI of 2   &   x = - 2 is B - 2 ,   - 8 Given A Q B P is a square m A Q · m A P = - 1 b a + 2 × 4 - 4 = - 1 a + 2 = b Also P Q must be parallel to x - axis thus, b = - 4 a = -

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