Question

An equilateral triangle is inscribed in the parabola $y^2=8x$, with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is

• A. $24\sqrt{3}$ units
• B. $16\sqrt{3}$ units
• C. $8\sqrt{3}$ units
• D. $4\sqrt{3}$ units

Answer 1

Answer: (B)

Let $l$ be the length of an equilateral triangle.

Then, from above figure, we can say that $\left(\frac{\sqrt{3}}{2}l,\frac{l}{2}\right)$
will lie on parabola $y^2=8x$.
$\Rightarrow {\left(\frac{l}{2}\right)}^2=8\left(\frac{\sqrt{3}}{2}l\right)\Rightarrow l^2=16\sqrt{3}l\Rightarrow l=16\sqrt{3}$ units