Question

The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^2=8x$, with one of its vertices on the vertex of this parabola, is:

• A. $128\sqrt{3}$
• B. $192\sqrt{3}$
• C. $64\sqrt{3}$
• D. $256\sqrt{3}$

Answer 1

The correct option is B $192\sqrt{3}$



$A:(a\cos {30}^{\circ },a\sin {30}^{\circ })$ lies on the parabola $\frac{a^2}{4}=8\cdot \frac{a\cdot \sqrt{3}}{2}$
$\Rightarrow a=16\sqrt{3}$

Area of equilateral $△=\frac{\sqrt{3}}{4}{a}^2$
$△=\frac{\sqrt{3}}{4}\cdot 16\cdot 16\cdot 3$
$△=192\sqrt{3}$