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  4. The length of the side of an equilateral triangle inscribed in the parabola, y2=4 x so that one of its angular point is at the vertex is :

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Q. The length of the side of an equilateral triangle inscribed in the parabola, $y^2=4 x$ so that one of its angular point is at the vertex is :

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Solution:

$\tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{2}{ t } \Rightarrow t =2 \sqrt{3}$. Hence $\operatorname{side}=4 at =8 \sqrt{3} a$