The locus of a point represented by \( x=\frac{a}{2}\left(\frac{t+1...

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The locus of a point represented by \( x=\frac{a}{2}\left(\frac{t+1}{t}\right), y=\frac{a}{2}\left(\frac{t-1}{t}\right) \), where \( t \in R-\{0\} \), is
\( \mathrm{P} \)
(1) \( x^{2}+y^{2}=a^{2} \)
(2) \( x^{2}-y^{2}=a^{2} \)
(3) \( x+y=a \)
(4) \( x-y=a \)
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