Find locus of centroid of a triangle whose vertices are (a cos t,a sin t) ,(b sin t, -b cos t) and (1,0)

Question

where 't' is parameter.?

Answer 1

Calculate the centroid of a triangle with three vertices by using formula: C = [(x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3].

Substitute (x₁, y₁) = (a cos t, a sin t), (x₂, y₂) = (b sin t, -b cos t) and (x₃, y₃) = (1, 0) in the above formula.

C = [(a cos t + b sin t + 1)/3, (a sin t - b cos t + 0)/3]

C = [(a cos t + b sin t + 1)/3, (a sin t - b cos t)/3]