cmi-entrance 2013 QB2

cmi-entrance · India · ugmath 15 marks Differential equations Solving Separable DEs with Initial Conditions

A curve $C$ has the property that the slope of the tangent at any given point $( x , y )$ on $C$ is $\frac { x ^ { 2 } + y ^ { 2 } } { 2 x y }$. a) Find the general equation for such a curve. Possible hint: let $z = \frac { y } { x }$. b) Specify all possible shapes of the curves in this family. (For example, does the family include an ellipse?)

A curve $C$ has the property that the slope of the tangent at any given point $( x , y )$ on $C$ is $\frac { x ^ { 2 } + y ^ { 2 } } { 2 x y }$.\\
a) Find the general equation for such a curve. Possible hint: let $z = \frac { y } { x }$.\\
b) Specify all possible shapes of the curves in this family. (For example, does the family include an ellipse?)

Paper Questions

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