\[\begin{array}{1 1}(1)(4 ,4 )(-4 ,-4)&(2)(2 ,8 )(-2 , -8 )\\(3)(4 ,0 )(-4 , 0 )&(4)(8 , 0 )(-8 , 0)\end{array}\]

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The equation of the given rectangular hyperbola is $xy= 16$

$c^2=16$

$\large\frac{a^2}{2}$$=16$

$a^2=32=> a= \sqrt {32}$

$a=\sqrt {16 \times 2}=>a=4 \sqrt 2$

$\therefore $Vertices are $A \bigg( \large\frac{4 \sqrt 2}{\sqrt 2} ,\frac{4 \sqrt 2}{\sqrt 2}\bigg)$

$A' \bigg( \large\frac{-4 \sqrt 2}{\sqrt 2} ,\frac{-4 \sqrt 2}{\sqrt 2}\bigg)$

=>$(4 ,4 )(-4 ,-4)$

Hence 1 is the correct answer.

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