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The angle between the tangents drawn from the point 4 , 1 to the parabola x 2 = 4 y is

Options

  1. Aπ 6
  2. Bπ 4
  3. Cπ 3
  4. Dπ 2

Correct answer

C. π 3

Step-by-step solution

Equation of the tangent to the parabola x 2 = 4 y having slope m is x = y m + m This tangent passes through 4 , 1 . So, 4 = m + 1 m or m 2 - 4 m + 1 = 0 Now, angle between the tangents is given by tan ⁡ θ = m 1 - m 2 1 + m 1 m 2 = m 1 + m 2 2 - 4 m 1 m 2 1 + m 1 m 2 = 16 - 4 1 + 1 = 3 or θ = π 3

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