If $(h, k)$ is the new origin to be chosen to eliminate first degree terms from the equation $\mathrm{S} \equiv 2 x^2-x y-y^2-3 x+3 y=0$ by translation and if $\theta$ is the angle with which the axes are to be rotated about the origin in anticlockwise direction to eliminate xy-term from $\mathrm{S}=0$, then $\tan 2 \theta=$

• A

  $h+k$
• B

  $h-k$
• C

  $h k$
• Correct answer
  D

  $-\frac{h}{3 k}$

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