Hello, shenton!
Determine the distance between the vertices of the hyperbola xy = 8 Evidently, you've never met this type of hyperbola.
The graph looks like this: Code:

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The hyperbola is "tipped" at a 45° angle.
The x and yaxes are the asymptotes.
The vertices lie on the line y = x.
So we have: .x² = 8 . → . x = ±2√2
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The vertices are: .(2√2, 2√2) and (2√2, 2√2)