We have 2y2−xy−6x2=0 ⇒‌‌2y2−4xy+3xy−6x2=0 ⇒‌‌2y(y−2x)+3x(y−2x)=0 ⇒‌‌(y−2x)(2y+3x)=0 ∴ Equations of sides of triangle are x+y=1, y−2x=0,2y+3x=0 On solving the above equations, we get the vertices of triangle as (‌
1
3
,‌
2
3
),(0,0) and (−2,3) ∴ Centroid of triangle =(‌