If \( x=a\left(t+\frac{1}{t}\right) \) and \( y=a\left(t-\frac{1}{t...

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If \( x=a\left(t+\frac{1}{t}\right) \) and \( y=a\left(t-\frac{1}{t}\right) \), find \( \frac{d y}{d x} \)
P
(A) \( \frac{y}{x} \)
(B) \( \frac{x}{y} \)
(C) \( -\frac{y}{x} \)
(D) \( -\frac{x}{y} \)
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