A) \[\frac{{{x}^{2}}}{{{c}^{2}}}\]
B) \[\frac{{{x}^{3}}}{c}\]
C) \[\frac{{{y}^{2}}}{{{c}^{2}}}\]
D) \[\frac{-{{y}^{3}}}{{{c}^{2}}}\]
Correct Answer: D
Solution :
Given that,\[xy={{c}^{2}}\] \[\Rightarrow \] \[y=\frac{{{c}^{2}}}{x}\] On differentiating w.r.t.\[x,\]we get \[\frac{dy}{dx}=\frac{-{{c}^{2}}}{{{x}^{2}}}\] \[\therefore \]Subnormal\[=y\frac{dy}{dx}=y\left( \frac{-{{c}^{2}}}{{{x}^{2}}} \right)\] \[=\frac{-y{{c}^{2}}}{{{\left( \frac{{{c}^{2}}}{y} \right)}^{2}}}=\frac{-{{y}^{3}}}{{{c}^{2}}}\]
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