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No. The rectangular hyperbola does not pass through the origin but it represents inverse proportionality.
If a hyperbola is vertical, the asymptotes have a slope of m = +- a/b. If a hyperbola is horizontal, the asymptotes have a slope of m = +- b/a.
denominators
denominators
You cannot solve this single equation. You can either change the subject so that it gives x = 12/y or xy = 12, which is the equation of a rectangular hyperbola.