A straight line cuts off the intercepts OA = a and OB = b on the positive directions of x -axis and y -axis respectively. If the perpendicular from…

A straight line cuts off the intercepts $\displaystyle \mathrm{OA}=\mathrm{a}$ and $\displaystyle \mathrm{OB}=\mathrm{b}$ on the positive directions of $\displaystyle x$-axis and $\displaystyle y$-axis respectively. If the perpendicular from origin O to this line makes an angle of $\displaystyle \frac{\pi}{6}$ with positive direction of $\displaystyle y$-axis and the area of $\displaystyle \Delta \mathrm{OAB}$ is $\displaystyle \frac{98}{3} \sqrt{3}$, then $\displaystyle \mathrm{a}^2-\mathrm{b}^2$ is equal to :