AP EAMCET202521 May 2025Evening ShiftMathematicsParabolaActual

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

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Correct answer

C. 3

Step-by-step solution

Given, y^2=4 x [ a=1] General equation of parabola =y=m x+ a m [where, m is the slope] at (1,4) ; 4=m+ a m 4=m+ 1 m m^2-4 m+1=0 Let m₁ and m₂ are the roots. m₁+m₂=4 and m₁ m₂=1 Now, = |m₁-m₂ | |1+m₁ m₂ | = (m₁+m₂ )^2-4 m₁ m₂ 1+m₁ m₂ = (4)^2-4(1) 1+1 = 16-4 2 = 12 2 = 2 3 2 = 3 = 3 = 3

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