Locus of centroid of the triangle whose vertices are and

MATHEMATICS · Single correct · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Locus of centroid of the triangle whose vertices are

(a \cos t, a \sin t), (b \sin t, -b \cos t)

and

(1, 0)

, where

t

is a parameter, is (1)

(3x - y)^2 + (3y)^2 = a^2 - b^2

(2)

(3x - y)^2 + (3y)^2 = a^2 + b^2

(3)

(3x + y)^2 + (3y)^2 = a^2 + b^2

(4)

(3x + y)^2 + 3y^2 = a^2 - b^2