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JEE Main201910 Jan 2019Morning ShiftMathematicsParabolaActual

If the parabolas y 2 = 4 b x - c and y 2 = 8 a x have a common normal, then which one of the following is a valid choice for the ordered triad a , b , c

Options

  1. A1 , 1 , 3
  2. B1 2 , 2 , 0
  3. C1 2 , 2 , 3
  4. DAll of above

Correct answer

D. All of above

Step-by-step solution

Axis of both parabola is x -axis i.e. y = 0 . As we know, axis of parabola is always a normal to the parabola. Hence, for all values of a , b , c a common normal is present. Another Method: Normal to parabola y 2 = 4 a x is give by y = m x - 2 a m - a m 3 ∴ Normal to parabola y 2 = 4 b x - c is y = m x - c - 2 b m - b m 3 replacing   a   by   b   and   x   by   x - c = m x - 2 b + c m - b m 3             . . . 1 and normal to parabola y 2 = 8 a

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