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Question: An equilateral triangle is inscribed in the parabola y<sup>2</sup> = 4ax whose vertices are at the p...

An equilateral triangle is inscribed in the parabola y2 = 4ax whose vertices are at the parabola, then the length of its side is equal to –

A

8a

B

8a38a\sqrt{3}

C

a2a\sqrt{2}

D

None of these

Answer

8a38a\sqrt{3}

Explanation

Solution

P(l cos 300, l sin 300) = (l32,l2)\left( \frac{\mathcal{l}\sqrt{3}}{2},\frac{\mathcal{l}}{2} \right)

P lies on parabola y2 = 4ax

\ l24=4a(l32)\frac{\mathcal{l}^{2}}{4} = 4a\left( \frac{\mathcal{l}\sqrt{3}}{2} \right)̃ l = 8a38a\sqrt{3}