Let ^ n C _ r -1 =28, ^ n C _ r =56 and ^ n C _ r +1 =70 . Let A (4 t, 4 t), B (2 t,-2 t ) and C (3 r-n, r^2-n-1 ) be the vertices of a triangle A B C , where t is a parameter. If (3 x-1)^2+(3 y)^2= , is the locus of the centroid of triangle ABC , then equals

Step-by-step solution

. array l ^n C_ r-1 =28 ^n C_r=56 ^n C_ r+1 =70 array l ^n C_ r-1 ^n C_r array = 28 56 r n-r+1 = 1 2 ^n C_r ^n C_ r+1 = 56 70 r+1 n-r = 70 56 array n=8=3 h= 4 t+2 t+1 3 k= 4 t-2 t 3 3 h-1=4 t+2 t3 k-1=4 t-2 t aligned & (1)^2+(2)^2 & (3 h-1)^2+(3 k)^2=20 aligned Locus of centroid: (3 x-1)^2+(3 y)^2=20 =20