The differential equation of family of curves whose tangent form an angle of \[\pi /4\] with the hyperbola \[xy={{C}^{2}}\] is

\[\frac{dy}{dx}=-\frac{{{C}^{2}}}{{{x}^{2}}}\]

\[\frac{dy}{dx}=\frac{{{x}^{2}}+{{C}^{2}}}{{{x}^{2}}-{{C}^{2}}}\]

\[\frac{dy}{dx}=\frac{{{x}^{2}}-{{C}^{2}}}{{{x}^{2}}+{{C}^{2}}}\]

The differential equation of family of curves whose tangent form an an

1.	The differential equation of family of curves whose tangent form an angle of \[\pi /4\] with the hyperbola \[xy={{C}^{2}}\] is
A.	\[\frac{dy}{dx}=\frac{{{x}^{2}}+{{C}^{2}}}{{{x}^{2}}-{{C}^{2}}}\]
B.	\[\frac{dy}{dx}=\frac{{{x}^{2}}-{{C}^{2}}}{{{x}^{2}}+{{C}^{2}}}\]
C.	\[\frac{dy}{dx}=-\frac{{{C}^{2}}}{{{x}^{2}}}\]
D.	None of these
Answer» C. \[\frac{dy}{dx}=-\frac{{{C}^{2}}}{{{x}^{2}}}\]

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The differential equation of family of curves whose tangent form an angle of \[\pi /4\] with the hyperbola \[xy={{C}^{2}}\] is

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