Question

A locus is a curve traced out by a point which moves under certain geometrical conditions:To find the locus of a point first we assume the coordinates of the moving point as $(h,k)$ and then try to find a relation between $h$ and $k$ with the help of the given conditions of the problem. If there is any variable involved in the process then we eliminate them. At last, we replace $h$ by $x$ and $k$ by $y$ and get the locus of the point which will be an equation in $x$ and $y$.

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:

• A. $(3x-1{)}^2+(3y{)}^2=a^2-b^2$
• B. $(3x-1{)}^2+(3y{)}^2=a^2+b^2$
• C. $(3x+1{)}^2+(3y{)}^2=a^2+b^2$
• D. $(3x+1{)}^2+(3y{)}^2=a^2-b^2$

Answer 1

The correct option is B $(3x-1{)}^2+(3y{)}^2=a^2+b^2$