A) hyperbola
B) circle
C) ellipse
D) parabola
Correct Answer: A
Solution :
Given differentia equation is \[={{\left( 3.04\times {{10}^{-8}}cm \right)}^{3}}\] \[=2.81\times {{10}^{-23}}c{{m}^{3}}\] \[2xydy=({{x}^{2}}+1)dx+{{y}^{2}}dx\] \[=2.81\times {{10}^{-23}}c{{m}^{3}}\] \[\frac{xd\left( {{y}^{2}} \right)-{{y}^{2}}dx}{{{x}^{2}}}=\left( \frac{{{x}^{2}}+1}{{{x}^{2}}} \right),,dx\] \[=2.81\times {{10}^{-23}}c{{m}^{3}}\] \[\int{d\left( \frac{{{y}^{2}}}{x} \right)=\int{\left( 1+\frac{1}{{{x}^{2}}} \right)dx}}\] \[=2.81\times {{10}^{-23}}c{{m}^{3}}\] \[\frac{{{y}^{2}}}{x}=x-\frac{1}{x}+C\] \[=2.81\times {{10}^{-23}}c{{m}^{3}}\] \[{{y}^{2}}=\left( {{x}^{2}}-1+Cx \right)\] When x = 1, y = 0 Then, 0 = 1 ? 1 + C \[=2.81\times {{10}^{-23}}c{{m}^{3}}\] C = 0 \[\therefore \] The solution is \[{{x}^{2}}-{{y}^{2}}=1i.e.,\] hyperbola.
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