If `P Q R` is an equilateral triangle inscribed in the auxiliary circle of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1,(a > b),` and `P^(prime)Q^(prime)R '` is the correspoinding triangle inscribed within the ellipse, then the centroid of triangle `P^(prime)Q^(prime)R '` lies at center of ellipse focus of ellipse between focus and center on major axis none of these

Explanation

To solve the problem, we need to find the coordinates of the centroid of the triangle \( P'Q'R' \) inscribed in the ellipse given by the equation

\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]

where \( a > b \).

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