Question

Let $ABC$ be an equilateral triangle inscribed in the auxiliary circle of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b).A^{\prime }{B}^{\prime }{C}^{\prime }$ be corresponding triangle inscribed within the ellipse , then centroid of the trianlgle $A^{\prime }{B}^{\prime }{C}^{\prime }$ lies at:

• A. focus of ellipse
• B. any vertex of the ellipse
• C. centre of the ellipse
• D. none

Answer 1

The correct option is C centre of the ellipse

for, $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$

eqn of auxillary circle, $x^2+y^2=a^2$

Centroid of $A^{\prime }{B}^{\prime }{C}^{\prime }$ lies on centre of the ellipse.