The equation is an approximation to the wheel path - it ignores factors such as rake and the natural tilt that a bicycle takes when turning. 

A reasonable model of a bicycle path is to consider the following: 
1) The rear wheel is mounted on a rigid frame oriented in the direction the rear wheel is moving. 
2) The front wheel is mounted at distance L forwards of the rear wheel, on the same rigid frame, but can pivot on a vertical axis.

As a result, the rear wheel is always pointing directly at the front wheel, so you can consider that at any time $t$, if the rear wheel is at a point $R(t)$, then the the front wheel is at a point distance $L$ along a line tangent to $R(t)$.

Maybe the picture below will help.
[![enter image description here][1]][1] 


  [1]: https://i.sstatic.net/mLBPCKUD.png