Question

$A$n equilateral triangle is inscribed in the parabola $y^2=\frac{1}{2}x$ so that one of its vertex coincides with the vertex of the parabola. Then the length of its side is

• A. $\sqrt{3}$
• B. $2\sqrt{3}$
• C. $3\sqrt{3}$
• D. $4\sqrt{2}$

Answer 1

The correct option is A $\sqrt{3}$

Since, triangle is equilateral then the slope of one of side of the triangle is ${30}^0$ which passes through origin.

Therefore, its equation is $y=\frac{x}{\sqrt{3}}$

Its intersection with parabola is $(\frac{3}{2},\frac{\sqrt{3}}{2})$ and $(0,0)$

Therefore, length of side is $\sqrt{\frac{9}{4}+\frac{3}{4}}=\sqrt{3}$