Calculus

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What is the orthogonal trajectory of y^2 - x^2 = C ??

  • Calculus -

    Using implicit differentiation, find the slope of the tangents
    y'=x/y
    The slopes of the normals are therefore:
    y'=-y/x
    Rearrange and integrate
    ∫y'/y = ∫-1/x
    ln y = -ln x + C1
    ln y = -k ln x
    raise to the power of e:
    y=C/x
    This is the family of reciprocal curves, or rectangular hyperbolas.

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