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AP® Calculus AB-BC

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A Family of Curves

APCALC-ZL4ZHJ

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

A

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

B

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

C

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

D

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