The equation of a trajectory depends on the specific context and type of trajectory. Here are a few examples:

1. Projectile Motion:
- Horizontal trajectory: x(t) = v0x*t
- Vertical trajectory: y(t) = v0y*t - (1/2)_g_t^2
- Parabolic trajectory: y(x) = ax^2 + bx + c
2. Circular Motion:
- x(t) = r*cos(ωt + θ)
- y(t) = r*sin(ωt + θ)
3. Elliptical Motion:
- x(t) = a*cos(ωt + θ)
- y(t) = b*sin(ωt + θ)
4. Parametric Equations:
- x(t) = f(t)
- y(t) = g(t)

Where:

- x and y are the coordinates of the trajectory
- v0x and v0y are the initial velocities
- g is the acceleration due to gravity
- r is the radius
- ω is the angular frequency
- θ is the phase angle
- a and b are the semi-axes of the ellipse
- f and g are functions of time