Thank you for reporting, we will resolve it shortly
Q.
If $A (\cos \alpha, \sin \alpha), B (\sin \alpha,-\cos \alpha), C (1,2)$ are the vertices of a $\triangle ABC$, then as $\alpha$ varies, the locus of its centroid is -
Straight Lines
Solution:
Let $( h , k )$ be the centroid of triangle
$3 h =\cos \alpha+\sin \alpha+1$
$\Rightarrow(3 h-1)=\cos \alpha+\sin \alpha$........(1)
$3 k =\sin \alpha-\cos \alpha+2$
$\Rightarrow(3 k-2)=\sin \alpha-\cos \alpha$........(2)
square & add (1) & (2)
$9\left(x^2+y^2\right)+6(x-2 y)=-3$