Posted by **Nadine** on Monday, December 14, 2009 at 9:03am.

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

- Calculus -
**MathMate**, Monday, December 14, 2009 at 10:00am
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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