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Locus of the centroid of the triangle whose vertices are $(a \cos t, a \sin t), (b \sin t, - b \cos t)$ and (1, 0); where t is $a$ parameter is

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(3x−1)2+(3y)2=a2+b2

(3x+1)2+(3y)2=a2+b2

(3x+1)2+(3y)2=a2−b2

(3x−1)2+(3y)2=a2−b2

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detailed solution

Correct option is A

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

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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

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Locus of the centroid of the triangle whose vertices are $(a \cos t, a \sin t), (b \sin t, - b \cos t)$ and (1, 0); where t is $a$ parameter is