Locus of the centroid of a triangle whose vertices are ((1,0) .(a t, a t) ), ((b t,-b t) ) is (9 x^2+9 y^2-6 x=k ). Then, the value of (k ) is equal to

Step-by-step solution

Centroid is given by (x= x₁+x₂+x₃ 3 and y= y₁+y₂+y₃ 3 ) So, (x= 1+a t+b t 3 ) and (y= 0+a t+(-b t) 3 ) ( (3 x-1)=a t+b t ) ...(i) and (3 y=a t-b t ) ...(ii) Squaring and adding Eqs. (i) and (ii), we get ( aligned & 9 x^2-6 x+1+9 y^2=a^2+b^2 & 9 x^2+9 y^2-6 x=a^2+b^2-1 & k=a^2+b^2-1 aligned )