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JEE Main202229 Jun 2022Evening ShiftMathematicsParabolaActual

Let P : y 2 = 4 a x , a > 0 be a parabola with focus S .Let the tangents to the parabola P make an angle of π 4 with the line y = 3 x + 5 touch the parabola P at A and B . Then the value of a for which A , B and S are collinear is:

Options

  1. A8 only
  2. B2 only
  3. C1 4 only
  4. Dany a > 0

Correct answer

D. any a > 0

Step-by-step solution

Lines making angle π 4 with y = 3 x + 5 So using formula tan α = m 2 - m 1 1 + m 1 m 2 , we have slope - 2   &   1 2 . Which are perpendicular to each-other so, A ,   S ,   B are collinear for all a > 0 . (by property that perpendicular tangents will lie on directrix and chord of contact will pass through focus, so the points are collinear )

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