Show that the locus represented by `x=(1)/(2)a(t+(1)/(t)),y=(1)/(2)a(t-(1)/(t))` is a rectangular hyperbola.
Text Solution
AI Generated Solution
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: Square both equations
We start by squaring both \( x \) and \( y \):
1. \( x = \frac{1}{2} a \left( t + \frac{1}{t} \right) \)
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