$\triangle O A B$ is an equilateral triangle inscribed in the parabola $y^2=4 a x, a\gt0$ with $O$ as the vertex, then the length of the side of $\triangle \mathrm{OAB}$ is

• Correct answer
  A

  $8 \mathrm{a} \sqrt{3}$ unit
• B

  8 a unit
• C

  $4 \mathrm{a} \sqrt{3}$ unit
• D

  4a unit

Solution

Hint : Slope of $O A: M_{O A}=\tan 30^{\circ}=\frac{1}{\sqrt{3}}$ Equation of $O A: y=\frac{1}{\sqrt{3}} x$ from parabola and line $O A, \frac{x^2}{3}=4 a x$ $\Rightarrow x=12 a \Rightarrow y=4 \sqrt{3} a \therefore A B=2 \times 4 \sqrt{3} a=8 a \sqrt{3}$ unit

Hence, the correct answer is option: 'A'.