Answered

Arrange the hyperbolas in increasing order of the horizontal widths of their asymptote rectangles.

(Y-11)^2/7^2 - (x-2)^2/6^2 = 1

(Y-1)^2/5^2 - (x-7)^2/12^2 =1

(X-6)^2/8^2 - (y+2)^2/5^2 =1

(X-4)^2/2^2 - (y+2)^2/5^2 =1

(Y+5)^2/2^2 - (x+4)^2/3^2 =1

(Y+1)^2/2^2 - (x-1)^2/9^2 = 1

(X+7)^2/4^2 - (x-9)^2/9^2 = 1