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,.... 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 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 x_(1),x_(2),x_(3), are in A.P.and y_(1),y_(2),y_(3), are also in A.P.with same common difference then the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) form

If x_(1),x_(2),x_(3) as well as y_(1),y_(2),y_(3) are also in G.P. With the same common ratio,then the points (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) lies on

If x_(1), x_(2), x_(3) as well as y_(1), y_(2), y_(3) are in GP, with the same common ratio, then the points (x_(1),y_(1)), (x_(2),y_(2)) and (x_(3), y_(3))

Let X_(1), X_(2), X_(3)……. are in arithmetic progression with a common difference equal to d which is a two digit natural number. y_(1), y_(2), y_(3)……… are in geometric progression with common ratio equal to 16. Arithmetic mean of X_(1), X_(2)……..X_(n) is equal to the arithmetic mean of y_(1), y_(2)......y_(n) which is equal to 5. If the arithmetic mean of X_(6), X_(7)....X_(n+5) is equal to the arithmetic mean of y_(P+1), y_(P+2)......y_(P+n) then d is equal to

If a,x_(1),x_(2) are in G.P with common ratio r and b,y_(1),y_(2) are in G.P with common ratio s where s-r=2 , then the area of the triangle with vertices (a,b),(x_(1),y_(1)),(x_(2),y_(2)) is