Find The Locus Of The Centroid Of An Equilateral Triangle Inscribed In The Ellipse

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Question

Find the locus of the centroid of an equilateral triangle inscribed in the ellipse

None of these

diffcult

Solution

Correct option is

Let the vertices of the equilateral triangle P, Q and R and whose eccentric angles are α, β and γ.

Let the centroid of âˆ†PQR be (h, k) then

and,

âˆµ âˆ†PQR is equilateral.

∴ Centroid of the âˆ†PQR is same as the circumcentre.

âˆµ Circumcentre of âˆ†PQR be

Using (i) and (ii) then

Squaring and adding (iii) and (iv) we get

Hence locus of (h, k) is

.

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