question_answer

An equilateral triangle is inscribed in the parabola \[{{y}^{2}}=4ax\] whose vertices are at the parabola, then the length of its side is equal to

A)            8a   

B)            \[8a\sqrt{3}\]

C)            \[a\sqrt{2}\]                             

D)            None of these

Correct Answer: B

Solution :

           \[{{L}_{1}}=\sqrt{3}y-x=0\], solving \[{{L}_{1}}\]                    and \[{{S}_{1}}\equiv {{y}^{2}}-4ax=0\]                 Then \[y=4a\sqrt{3}\]and\[x=12a\]                    Hence \[L=\sqrt{144{{a}^{2}}+48{{a}^{2}}}\]                    \[=a\sqrt{192}=8a\sqrt{3}\].