A) \[\frac{y}{x}\]
B) \[\frac{-y}{x}\]
C) \[\frac{x}{y}\]
D) \[\frac{-x}{y}\]
Correct Answer: C
Solution :
\[x=a\left( t-\frac{1}{t} \right)\] ....(i) and \[y=a\left( t+\frac{1}{t} \right)\] .....(ii) Squaring (i) and (ii), then subtracting we get, \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}(-4)\] or \[{{y}^{2}}-{{x}^{2}}=4{{a}^{2}}\] Differentiating both sides w.r.t. x, \[2y\frac{dy}{dx}-2x=0\]Þ \[\frac{dy}{dx}=\frac{x}{y}\].
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