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NTA Abhyas JEE Main2020MathematicsParabolaPractice

The point of intersection of the tangent to the parabola y 2 = 4 x which also touches x 2 + y 2 = 1 2 is

Options

  1. A- 1 , 0
  2. B- 1 2 , 0
  3. C- 2 , 0
  4. D- 3 2 , 0

Correct answer

A. - 1 , 0

Step-by-step solution

Equation of the tangent to the parabola is y = m x + 1 m Equation of the tangent to the circle is y = m x ± 1 2 1 + m 2 For common tangent 1 m 2 = 1 2 1 + m 2 ⇒ m 4 + m 2 - 2 = 0 ⇒ m 2 = 1 ⇒ m = ± 1 ⇒ Equation of the tangents are y = x + 1 and y = - x - 1 ⇒ Point of intersection of these tangents is - 1 , 0

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