A) \[(1-{{y}^{2}})={{c}^{2}}(1-{{x}^{2}})\]
B) \[(1+{{y}^{2}})={{c}^{2}}(1-{{x}^{2}})\]
C) \[(1+{{y}^{2}})={{c}^{2}}(1+{{x}^{2}})\]
D) None of these
Correct Answer: A
Solution :
Given equation can be written as \[\frac{x}{1-{{x}^{2}}}dx=\frac{y}{1-{{y}^{2}}}dy\] On integrating we get \[-\frac{1}{2}\log (1-{{x}^{2}})=-\frac{1}{2}\log (1-{{y}^{2}})+\log c\] Þ \[\log (1-{{x}^{2}})-\log (1-{{y}^{2}})=-2\log c\] Þ \[\frac{1-{{x}^{2}}}{1-{{y}^{2}}}={{c}^{-2}}\] Hence \[(1-{{y}^{2}})={{c}^{2}}(1-{{x}^{2}})\].
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