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JEE Main20207 Jan 2020Morning ShiftMathematicsParabolaActual

If y = m x + 4 is a tangent to both the parabolas, y 2 = 4 x and x 2 = 2 b y , then b is equal to

Options

  1. A- 32
  2. B- 64
  3. C- 128
  4. D128

Correct answer

C. - 128

Step-by-step solution

Equation of tangent to y 2 = 4 a x in slope Form is y = m x + a m . Comparing with given equation of tangent and parabola we get 1 m = 4 ⇒ m = 1 4 . Hence, line y = x 4 + 4 is tangent to x 2 = 2 b y also. Solving both, we get x 2 = 2 b x 4 + 4 ⇒ 2 x 2 - b x - 16 b = 0   . . ( 1 ) . Since the line is a tangent, so 1 must have equal roots. ⇒ - b 2 - 4 · 2 · - 16 b = 0 ⇒ b 2 + 128 b = 0 ⇒ b = 0 , - 128 But b can't be zero. So, b = - 128

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