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

In Advanced Level Maths, the equations of linear motion are:

1. Constant Acceleration:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

1. Uniform Motion:
- s = vt
- v = s/t

Where:
s = distance
v = constant velocity
t = time

1. Motion with Variable Acceleration:
- dv/dt = a(t)
- v = ∫a(t)dt
- s = ∫v(t)dt

Where:
a(t) is the acceleration function
v(t) is the velocity function
s(t) is the position function

These equations describe linear motion in one dimension. In two or three dimensions, vector equations are used to describe motion.

In Advanced Level Maths, the equations of linear motion are:

1. Constant Acceleration:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

1. Uniform Motion:
- s = vt
- v = s/t

Where:
s = distance
v = constant velocity
t = time

1. Motion with Variable Acceleration:
- dv/dt = a(t)
- v = ∫a(t)dt
- s = ∫v(t)dt

Where:
a(t) is the acceleration function
v(t) is the velocity function
s(t) is the position function

These equations describe linear motion in one dimension. In two or three dimensions, vector equations are used to describe motion.

In Advanced Level Maths, the equations of linear motion are:

1. Constant Acceleration:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

1. Uniform Motion:
- s = vt
- v = s/t

Where:
s = distance
v = constant velocity
t = time

1. Motion with Variable Acceleration:
- dv/dt = a(t)
- v = ∫a(t)dt
- s = ∫v(t)dt

Where:
a(t) is the acceleration function
v(t) is the velocity function
s(t) is the position function

These equations describe linear motion in one dimension. In two or three dimensions, vector equations are used to describe motion.

Here are the geometrical rules for drawing ray diagrams:

1. *Incident ray*: Draw a straight line from the object to the mirror/lens.
2. *Normal*: Draw a perpendicular line to the mirror/lens at the point of incidence.
3. *Reflected ray*: Draw a straight line from the mirror/lens to the image, making the same angle with the normal as the incident ray.
4. *Refraction*: Draw a straight line from the object to the lens, and another from the lens to the image, bending at the lens surface.
5. *Virtual image*: Draw a dashed line from the mirror/lens to the virtual image, behind the mirror/lens.
6. *Real image*: Draw a solid line from the mirror/lens to the real image, in front of the mirror/lens.
7. *Object distance*: Measure from the mirror/lens to the object.
8. *Image distance*: Measure from the mirror/lens to the image.

Remember to use a ruler and protractor to ensure accuracy!

Let me know if you have any specific questions or need help with a ray diagram!