Let the coordinates of the centroid be G(x,y) of the △APQ is x=
xA+xP+xQ
3
,y=
yA+yP+yQ
3
Given the points A(a,0),P(acosθ,asinθ) and Q(bsinθ,−bcosθ) The coordinates of the centroid are x=
a+acosθ+bsinθ
3
y=
0+asinθ−bcosθ
3
Let x=h and y=k, then, h=
a+acosθ+bsinθ
3
,k=
asinθ−bcosθ
3
⇒3h−a=acosθ+bsinθ 3k=asinθ−bcosθ Squaring and adding these equations (3h−a)2+(3k)2=(acosθ+bsinθ)2+(asinθ−bcosθ)2 =a2cos2θ+b2sin2θ+2abcosθsinθ+a2sin2θ+b2cos2θ−2abcosθsinθ =a2+b2 Replacing h with x and k with y, we get the locus of the centroid as (3x−a)2+(3y)2=a2+b2 ⇒(x−