Any curve with the property that whenever it intersects a curve of a given family it does so at an angle a ≠ π/2 is called an oblique trajectory of the given family. (See Figure 1.1.6.) Let m1 (equal to tan a1) denote the slope of the required family at the point (x, y), and let m2 (equal to tan a2) denote the slope of the given family. Show that
[Hint: From Figure 1.1.6, tan a1 = tan(a2 −a). Thus, the equation of the family of oblique trajectories is obtained by solving
Figure 1.1.6: Oblique trajectories intersecting at an angle a.
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