Given equation of parabola, y2=16x and all the vertices are of an equilateral triangle with one of them coincides with the vertex of parabola
Since, given parabola is symmetrical about X -axis So, ∠AOM=30∘ In
△AOM,tan30∘=
AM
OM
=
8t
4t2
⇒
1
√3
=
2
t
⇒t=2√3
∴ Coordinate of point A lying on parabola is (4(2√3)2,8(2√3))≡(48,16√3) ∴ Distance OA=√(xA−x0)2+(yA−y0)2 =√(48−0)2+(16√3−0)2 OA=32√3 ∴ Length of the side of equilateral triangle =32√3.