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The angle between the tangents drawn from the point 2,6 to the parabola y 2 - 4 y - 4 x + 8 = 0 is

Options

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

Correct answer

C. π 3

Step-by-step solution

Given parabola is y - 2 2 = 4 x - 1 Equation of tangent in slope form to this parabola is y - 2 = m x - 1 + 1 m It passes through 2,6 , so 4 = m + 1 m ⇒ m 2 - 4 m + 1 = 0 If m 1 and m 2 are roots of this equation, then m 1 + m 2 = 4 ,   m 1 · m 2 = 1 The angle between the tangents = tan - 1 ⁡ m 1 - m 2 1 + m 1 m 2 = tan - 1 ⁡ m 1 + m 2 2 - 4 m 1 m 2 1 + m 1 m 2 = tan - 1 ⁡ 16 - 4 2 = tan - 1 3 = π 3

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