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

The hyperbolas in increasing order of the horizontal widths of their asymptote rectangles are:

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

↓

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

↓

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

↓

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

↓

(x-6)^2/8^2-(y+1)^2/3^2=1

↓

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

↓

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

Step-by-step explanation:

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

Vertical hyperbola

Horizontal width of its asymptote rectangle is 2b

b^2=6^2→b=6

2b=2(6)→2b=12

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

Vertical hyperbola

Horizontal width of its asymptote rectangle is 2b

b^2=12^2→b=12

2b=2(12)→2b=24

3. (x-6)^2/8^2-(y+1)^2/3^2=1

Horizontal hyperbola

Horizontal width of its asymptote rectangle is 2a

a^2=8^2→a=8

2a=2(8)→2a=16

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

Horizontal hyperbola

Horizontal width of its asymptote rectangle is 2a

a^2=2^2→a=2

2a=2(2)→2a=4

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

Vertical hyperbola

Horizontal width of its asymptote rectangle is 2b

b^2=3^2→b=3

2b=2(3)→2b=6

6. (y+1)^2/2^2-(x-1)^2/9^2=1

Vertical hyperbola

Horizontal width of its asymptote rectangle is 2b

b^2=9^2→b=9

2b=2(9)→2b=18

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

Horizontal hyperbola

Horizontal width of its asymptote rectangle is 2a

a^2=4^2→a=4

2a=2(4)→2a=8

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step-by-step explanation:

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