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If an equilateral triangle is inscribed in a parabola $y^{2} = 12 x$ with one of the vertex being at the vertex of its parabola then its height is

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answer is C.

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Detailed Solution

$T a n 30^{o} = \frac{y}{x}$ $\Rightarrow x = y \sqrt{3}$

$y^{2} = 12 x$

$\frac{x^{2}}{3} = 12 x$ $\Rightarrow x = 36$

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