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AP EAMCET201921 Apr 2019Morning ShiftMathematicsParabolaActual

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

Options

  1. A4
  2. B3
  3. C2 5
  4. D6

Correct answer

B. 3

Step-by-step solution

Equation of a tangent to a parabola y^2=4 x is y=m x+ 1 m Since, it passes through point (1,4) . So, or 4=m+ 1 m array ll & m^2-4 m+1 & m= 4 16-4 2 = 4 12 2 & m=2 3 & m₁=2+ 3 and m₂=2- 3 array Hence, angle between two slopes is aligned & = | m₁-m₂ 1+m₁ m₂ |= | 2 3 1+1 | & = 3 aligned aligned & & = 3 & & = 3 aligned

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