Let the centroid be G(x,y). The coordinates of the centroid of triangles with vertices (x1,y1),(x2,y2) and (x3,y3) are x=‌
x1+x2+x3
3
and y=‌
y1+y2+y3
3
Substituting the coordinates of A,B and P. x=‌‌
2+3+t
3
=‌
5+t
3
y=‌‌
3+2+t2
3
=‌
5+t2
3
⇒3x−5=t,y=‌
5+(3x−5)2
3
‌(∵t=2x−5) ⇒3y=5+9x2+25−30x ⇒9x2−30x−3y+30=0 ⇒3x2−10x−y+10=0 The equation of the locus of the centroid of △ABC is 3x2−10x−y+10=0