Graph: xy = 12

<strong>Graph</strong>: <strong>xy</strong> = <strong>12</strong><br />

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<strong>xy</strong> = <strong>12</strong> is equivalent to y = <strong>12</strong>/x.<br />

The graph of this equation is called a<br />

'hyperbola'.<br />

Its asymptotes are the x and y axes.<br />

Any equation of the form<br />

is an inverse variation, and its graph will be a<br />

hyperbola with asymptotes at the x and y axes.<br />

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The translation of<br />

is<br />

The asymptotes are x = h and y = k.<br />

The domain is all reals except h. x ≠ h<br />

The range is all reals except k. y ≠ k<br />

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asymptotes:<br />

x = 2<br />

y = 4<br />

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An equation of the form<br />

will also have a graph that is a hyperbola.<br />

Its asymptotes are:<br />

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Here's why -<br />

x-asymptote:<br />

y-asymptote:<br />

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asymptotes:<br />

x = 3<br />

y = 2<br />

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