A) \[{{x}^{2}}\]
B) \[{{x}^{3}}\]
C) \[{{y}^{2}}\]
D) \[{{y}^{3}}\]
Correct Answer: D
Solution :
\[xy={{c}^{2}}\] ?..(i) \[\because \] Subnormal = \[y\frac{dy}{dx}\] \ From (i), \[y=\frac{{{c}^{2}}}{x}\] Þ \[\frac{dy}{dx}=\frac{-{{c}^{2}}}{{{x}^{2}}}\] \Subnormal\[=\frac{y\times (-{{c}^{2}})}{{{x}^{2}}}=\frac{-y{{c}^{2}}}{{{\left( \frac{{{c}^{2}}}{y} \right)}^{2}}}=\frac{-y{{c}^{2}}{{y}^{2}}}{{{c}^{4}}}=\frac{-{{y}^{3}}}{{{c}^{2}}}\] \ Subnormal varies as \[{{y}^{3}}.\]
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