An equilateral triangle is inscribed in the parabola y2=4ax, such that one vertex of this triangle coincides with the vertex of the parabola. Side length of this triangle is
8a√3
If triangle OAB is equilateral then OA = OB = AB. Thus AB will be a double ordinate of the parabola.
∠AOX=∠XOB=π6Let A=(at21,2at1)then B=(at21,−2at1)Slope of OA=2t1=1√3⇒t1=2√3⇒AB=4at1=8a√3 units