Ok, you've got a few more variables in there than I'm used to seeing... I'm not entirely certain where t, u, b and c come into this.

right now, I'm calculating my parabola

y=ax^2

where A is half the distance between the focus and the directrix...

with the 'ray' I have the origin (x,y) and the slope (s)... not certain how to plug that in to what you posted as I've no clue what t and u are in your example.

is u in your example simply 1/t? What are your b and c defined as?

... and thanks for the help - I've got a very basic understanding of what I'm trying to do here... A LOT of the formula's in the books on the subject seem to prattle on and on about theory without any examples of actual application. (Yes, I'm an impatient sort who threw away the 'users guide' in the TP releases and dove right for the 'language reference' book)