Upgrade subject to access all content

Which of the following represents the family of curves for which the slope of the tangent at any point $(x,y)$ on it is $\cfrac{{ ( { x }^{ 2 }+{ y }^{ 2 } ) }}{{ 2xy }}$?

${ x }^{ \\\ 2 }+{ y }^{ 2 }=C$

${ x }^{ \\\ 2 }-{ y }^{ 2 }=Cx$

${ x }^{ \\\ 2 }+{ y }^{ 2 }=Cx$

${ y }^{ \\\ 2 }-{ x }^{ 2 }=Cx$