The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8 x , with one of its vertices on the vertex of this parabola is

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y 2 = 8 x , a = 2 A ≡ 2 t 2 , 2 ( 2 ) t ≡ 2 t 2 , 4 t tan 30 ° = 4 t 2 t 2 = 2 t = 1 3 t = 2 3 Area of Δ OAB = 2 · Δ OMA = 2 · 1 2 · 2 t 2 ( 4 t ) = 8 t 3 = 8 ( 2 3 ) 3 = 192 3

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