Which one of the following differential equation represents the family of straight lines which are at unit distance from the origin?

Question

TuteeHUB · Accepted Answer

${\left( {{\rm{y}} + {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 - {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}$

TuteeHUB · Answer

${\left( {{\rm{y}} - {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 - {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}$

TuteeHUB · Answer

${\left( {{\rm{y}} + {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 + {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}$

TuteeHUB · Answer

${\left( {{\rm{y}} - {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 + {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}$

1.	Which one of the following differential equation represents the family of straight lines which are at unit distance from the origin?
A.	\({\left( {{\rm{y}} - {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 - {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}\)
B.	\({\left( {{\rm{y}} + {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 + {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}\)
C.	\({\left( {{\rm{y}} - {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 + {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}\)
D.	\({\left( {{\rm{y}} + {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 - {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}\)
Answer» D. \({\left( {{\rm{y}} + {\rm{x}}\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2} = 1 - {\left( {\frac{{{\rm{dy}}}}{{{\rm{dx}}}}} \right)^2}\)

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