The differential equation which represents the three parameter family of circles\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is

\[y'''=\frac{3y'{{'}^{2}}}{1+y{{'}^{2}}}\]

\[y'''=\frac{3y'y'{{'}^{2}}}{1+y{{'}^{2}}}\]

\[y'''=\frac{3y'}{1+y{{'}^{2}}}\]

\[y'''=\frac{3y'}{1-y{{'}^{2}}}\]

The differential equation which represents the three parameter family

1.	The differential equation which represents the three parameter family of circles\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is
A.	\[y'''=\frac{3y'y'{{'}^{2}}}{1+y{{'}^{2}}}\]
B.	\[y'''=\frac{3y'{{'}^{2}}}{1+y{{'}^{2}}}\]
C.	\[y'''=\frac{3y'}{1+y{{'}^{2}}}\]
D.	\[y'''=\frac{3y'}{1-y{{'}^{2}}}\]
Answer» B. \[y'''=\frac{3y'{{'}^{2}}}{1+y{{'}^{2}}}\]

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The differential equation which represents the three parameter family of circles\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is

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