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Show that the locus represented by x=(1)...

Show that the locus represented by `x=(1)/(2)a(t+(1)/(t)),y=(1)/(2)a(t-(1)/(t))` is a rectangular hyperbola.

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To show that the locus represented by the equations \( x = \frac{1}{2} a \left( t + \frac{1}{t} \right) \) and \( y = \frac{1}{2} a \left( t - \frac{1}{t} \right) \) is a rectangular hyperbola, we will follow these steps: ### Step 1: Express \( x \) and \( y \) in terms of \( t \) Given: \[ x = \frac{1}{2} a \left( t + \frac{1}{t} \right) \] ...
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