This exercise is intended to find the minimal distance required for a parallel parking spot (beyond the length of the car itself). Adjust the sliders to see how the various parameters affect the outcome. Note that d_c is the distance you're allowing to exist between the parked car and the parallel curb. Setting d_c to zero would have the car positioned flush against the curb at the end of its backward motion. Setting d_c to a positive value allows the car to pull forward in order to straighten out after initially backing up. Intuitively, the larger you set d_c to be, the less distance you need to fit between the parked cars.
Note that the angle alpha is also critical to a good parallel parking job. Check the "optimize" box to use the value of alpha that will minimize the required parking space.
Note: Setting both d_c and alpha to zero reduces my model to Professor Blackburn's model, but I find this to be overly conservative.