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JEE Main20206 Sep 2020Morning ShiftMathematicsParabolaActual

Let L 1 be a tangent to the parabola y 2 = 4 ( x + 1 ) and L 2 be a tangent to the parabola y 2 = 8 ( x + 2 ) such that L 1 and L 2 intersect at right angles. Then L 1 and L 2 meet on the straight line:

Options

  1. Ax + 3 = 0
  2. B2x + 1 = 0
  3. Cx + 2 = 0
  4. Dx + 2y = 0

Correct answer

A. x + 3 = 0

Step-by-step solution

Let tangent of y 2 = 4 ( x + 1 ) be L 1 : t 1 y = ( x + 1 ) + t 1 2 and tangent of y 2 = 8 ( x + 2 ) be L 2 : t 2 y = ( x + 2 ) + 2 t 2 2 L 1 ⊥ L 2 1 t 1 · 1 t 2 = - 1 t 1 t 2 = - 1 t 2 × ( i ) - t 1 × ( i i )    ⇒    x + 3 = 0

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