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The locus of centroid of the triangle whose vertices are (a cost, a sint), (b sint, -b cost) and (1, 0) where ‘t’ is a parameter is

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${(3 x - 1)}^{2} + {(3 y)}^{2} = a^{2} - b^{2}$

${(3 x + 1)}^{2} + {(3 y)}^{2} = a^{2} - b^{2}$

${(3 x + 1)}^{2} + {(3 y)}^{2} = a^{2} + b^{2}$

${(3 x - 1)}^{2} + {(3 y)}^{2} = a^{2} + b^{2}$

answer is B.

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Detailed Solution

$3 G = A + B + C \Rightarrow (3 x, 3 y) = (a \cos t + b \sin t + 1, a \sin t - b \cos t)$

$∴ {(3 x - 1)}^{2} + {(3 y)}^{2} = a^{2} + b^{2}$

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