Locus of a centriod 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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x = 3 c o s t + b s i n t + 1 ​ ⇒ a cos t + b sin t = 3 x − 1 y = 3 a s i n t − b c o s t ​ ⇒ a sin t − b sin t = 3 y Squaring \& adding, ( 3 x − 1 ) 2 + ( 3 y ) 2 = a 2 + b 2

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