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  4. The area (in sq. units) of an equilateral triangle inscribed in the parabola y2=8 x, with one of its vertices on the vertex of this parabola, is :

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Q. 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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Solution:

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$\tan 30^{\circ}=\frac{4 t }{2 t ^{2}}=\frac{2}{ t } \Rightarrow t =2 \sqrt{3}$
$AB =8 t =16 \sqrt{3}$
Area $=256.3 \cdot \frac{\sqrt{3}}{4}=192 \sqrt{3}$