A) \[(2,2)\]
B) \[(2,3)\]
C) \[(2,-2)\]
D) None of these
Correct Answer: A
Solution :
[a] We have \[\frac{dy}{dx}=\frac{\sqrt{{{y}^{4}}-{{y}^{2}}}}{\sqrt{{{x}^{4}}-{{x}^{2}}}}=\frac{y\sqrt{{{y}^{2}}-1}}{x\sqrt{{{x}^{2}}-1}}\] \[\Rightarrow \,\,\,\int{\frac{dy}{y\sqrt{{{y}^{2}}-1}}}\int{\frac{dx}{x\sqrt{{{x}^{2}}-1}}}\] \[\Rightarrow \,\,\,\,{{\sec }^{-1}}y={{\sec }^{-1}}x+c\] Since \[y(0)=0,\,\,c=0.\] \[\therefore \,\,\,\,{{\sec }^{-1}}y={{\sec }^{-1}}\,\,x\] or \[y=x\]
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