A) \[\frac{1}{2}\]
B) \[1.0\text{ }g\,c{{m}^{-3}},\]
C) \[90.0\text{ }g\,mo{{l}^{-1}}\]
D) \[\text{115}\text{.0 }g\,mo{{l}^{-1}}\]
Correct Answer: C
Solution :
Use the general equation of circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]and eliminate g. General equation of all such circles which pass through the origin and whose centre lie on x-axis, is \[{{x}^{2}}+{{y}^{2}}+2gx=0\] ...(i) On differentiating w.r.t.\[x,\]we get \[2x+2y\frac{dy}{dx}+2g=0\] \[\Rightarrow \]\[2g=-\left( 2x+2y\frac{dy}{dx} \right)\] On putting the value of 2 g in Eq. (i), we get \[{{x}^{2}}+{{y}^{2}}+\left( -2x-2y\frac{dy}{dx} \right)=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-2{{x}^{2}}-2xy\frac{dy}{dx}=0\] \[\Rightarrow \] \[{{y}^{2}}={{x}^{2}}+2xy\frac{dy}{dx}\] which is required equation.
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