Isogonal trajectory

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When a family of curves intersects another family at a specific constant angle α, the first family is referred to as an isogonal family of the second one, and in this case it is said that every family is an isogonal trajectory of the other. It is assumed that α is different from π/2; if α=п/2 both families are orthogonal. If the given family is described by the differential equation

\frac{dy}{dx} = f(x,y),

then the isogonal family satisfies the differential equation

\frac{dy}{dx} = \frac{f(x,y)+\tan\alpha}{1-f(x,y)\tan\alpha}.
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