If $\mathrm{A}(\cos \alpha, \sin \alpha), \mathrm{B}(\sin \alpha,-\cos \alpha), \mathrm{C}(1,2)$ are the vertices of a $\triangle \mathrm{ABC}$ then the locus of its centroid is

• Correct answer
  A

  $3\left(x^2+y^2\right)-2 x-4 y+1=0$
• B

  $x^2+y^2-2 x-4 y+1=0$
• C

  $x^2+y^2-2 x-4 y+3=0$
• D

  $2\left(x^2+y^2\right)-2 x-4 y+5=0$

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