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AP® Calculus AB-BC

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Moderate

Differential Equations: Orthogonal Curves

APCALC-2J1RLJ

Which of the following equations represents a curve that intersects every curve of the family $y = \cfrac {1}{x^2} + m$, where $m$ can be any real number?

A

$y = \cfrac {x^4}{8}$

B

$y = \cfrac {x^3}{2}$

C

$y = \ln {x^2} + kx$

D

$y = -\cfrac {2}{x^3}$