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AP EAMCET202023 Sep 2020Morning ShiftMathematicsParabolaActual

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

Options

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

Correct answer

C. π 3

Step-by-step solution

As we know that any tangent to the parabola y 2 = 4 x is y = m x + 1 m ∵ Tangents are passing through the points 1 , 4 ⇒ 4 = m + 1 m ⇒ m 2 - 4 m + 1 = 0 Let the roots be m 1 and m 2 ⇒ m 1 + m 2 = 4 and m 1 m 2 = 1 Now, m 1 - m 2 2 = m 1 + m 2 2 - 4 m 1 m 2 = 16 - 4 = 12 ⇒ m 1 - m 2 = 2 3 Now, angle between tangents is tan θ = m 1 - m 2 1 + m 1 m 2 ⇒ tan θ = 2 3 2 = 3 ⇒ θ = π 3

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