If the lines represented by $x^2-2 h x y-y^2=0$ are rotated about $(0,0)$ through an angle $\alpha$ one in clockwise direction and the other in the counter clockwise direction, then the combined equation of the bisectors of the angle between the lines thus obtained is

• A

  $x^2-y^2+h x y=0$
• B

  $x^2-2 h x y+y^2=0$
• Correct answer
  C

  $h x^2-h y^2+2 x y=0$
• D

  $h x^2+h y^2-x y=0$

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