Any curve with the property that whenever it intersects a curve of a given family it doe...

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.