The angle between the tangents drawn from the point (1,4) to the parabola y2=4x is

y=mx+1mThe above tangent passes through (1, 4). So, 4=m+1m or  m2−4m+1=0Now, angle between the lines is given bytan⁡θ=m1−m21+m1m2 =m1+m22−4m1m21+m1m2=16−41+1=3 or  θ=π3