If `a,x_1,x_2,....` and `b,y_1,y_2...` form two infinite G.P's with same common ratio 'r' then the locus of `P(h,k)` when `h= (x_1x_2x_3...x_n)^(1/n)` and `k=(y_1y_2y_3.....y_n)^(1/n)` is

If a,x_(1),x_(2),x_(3),... .and b,y_(1),y_(2)...... form two infinite geometric prograssions with same common ratio 'r' then the locus of p(h,k) when h=root(n)(x_(1)x_(2)...x_(n)) and k=root(n)(y_(1)y_(2)..... y_(n)) is.

If a,x_(1), x_(2), x_(3) …..and b, y_(1), y_(2) , …..form two infinite A.P's with common difference p and q respectively then the locus of P(h, k) when h=(x_(1)+x_(2)+x_(3)……+x_(n))/(n) , k=(y_(1)+y_(2)+……..+y_(n))/(n) is

If x_1, x_2 , x_3 and y_1 , y_2 , y_3 are both in G.P. with the same common ratio, then the points (x_1 , y_1),(x_2 , y_2) and (x_3 , y_3)

If p,x_(1),x_(2),x_(3)... and q,y_(1),y_(2),y_(3),... from two infinite AP's with common difference a and b respectively.Then locus of p(alpha,beta) where alpha=((1)/(n))[x_(1)+x_(2)+x_(3)+...+x_(n)] and beta=((1)/(n))[y_(1)+y_(2)+y_(3)+...y_(n)] is

If x_(1),x_(2),x_(3) and y_(1),y_(2),y_(3) are both in G.P. with the same common ratio then the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3))

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m

If x_1,x_2,x_3 as well as y_1, y_2, y_3 are in G.P. with same common ratio, then prove that the points (x_1, y_1),(x_2,y_2),a n d(x_3, y_3) are collinear.