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NTA Abhyas JEE Main2020MathematicsParabolaPractice

The line y = 2 x + C is a tangent to the parabola y 2 − 4 y − 8 x = 4 at a point whose abscissa is α , then the ordered pair α , C is

Options

  1. A− 1 2 , 4
  2. B− 1 2 , 5
  3. C4 ,   5
  4. D− 1 2 , 1 2

Correct answer

B. − 1 2 , 5

Step-by-step solution

Equation of parabola is y − 2 2 = 8 x + 1 So, equation of tangent with slope 2 is y − 2 = 2 x + 1 + 2 2 ⇒ y = 2 x + 5 ⇒ C = 5 Point of contact is − 1 2 , 4 ⇒ α = − 1 2

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