A) \[\frac{y}{x}\]
B) \[-\frac{y}{x}\]
C) \[-\frac{x}{y}\]
D) \[\frac{x}{y}\]
Correct Answer: B
Solution :
\[\frac{dx}{dt}=\frac{1}{2\sqrt{{{2}^{\cos e{{c}^{-1}}t}}}}\]\[{{2}^{^{\cos e{{c}^{-1t}}}}}\log 2.\frac{-1}{x\sqrt{{{x}^{2}}-1}}\] \[\frac{dy}{dt}=\frac{1}{2\sqrt{{{2}^{{{\sec }^{-1t}}}}}}{{2}^{{{\sec }^{-1t}}}}\log 2.\frac{1}{x\sqrt{{{x}^{2}}-1}}\] Thus \[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{-\sqrt{{{2}^{{{\operatorname{cosec}}^{-1}}t}}}}{\sqrt{{{2}^{{{\sec }^{-1t}}}}}}\frac{{{2}^{{{\sec }^{-1}}t}}}{{{2}^{\cos e{{c}^{-1}}t}}}\] \[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\sqrt{\frac{{{2}^{{{\sec }^{-1}}t}}}{{{2}^{\cos e{{c}^{-1}}t}}}}=\frac{-y}{x}\]
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