Locus of the centroid of the triangle whose vertices are (acos⁡t,asin⁡t),(bsin⁡t,−bcos⁡t) and  (1, 0); where t is a parameter is

If (h, k) is the centroid, thenh=acos⁡t+bsin⁡t+13k=asin⁡t−bcos⁡t+03⇒(3h−1)2+(3k)2=(acos⁡t+bsin⁡t)2+(asin⁡t−bcos⁡t)2Locus of =a2+b2(h,k) is (3x−1)2+(3y)2=a2+b2