In this paper, we propose a new model for lane tracking and curve detection. We use a linear-parabolic model for each lane boundary, and apply constraints to link both lane boundaries based on the expected geometry of the road. The parabolic part of the model, which fits the far field, is then used to analyze the geometry of the road ahead (straight, right curve or left curve), with applications in driver?s assistance systems and road inspection. Experimental results indicate that introduced geometric constraints result in a more consistent fit if compared to the individual fitting of each lane boundary, and that the parabolic part of the model can be effectively used to keep the driver informed about the geometry of the road in front of him/her.