
    Calculate the horizontal line (directrix) in the city's coordinate system where the ratio of distance between any point on the ride-sharing demand curve and a central focal point equals the distance from that same point to this line. Given the demand distribution parameters of vertical scaling (a), geographical offset (b), and baseline activity level (c), determine this critical boundary line that helps optimize driver positioning across the service area.
    

    
def parabola_directrix(a, b, c):
    """
    Calculate the horizontal line (directrix) in the city's coordinate system where the ratio of distance between any point on the ride-sharing demand curve and a central focal point equals the distance from that same point to this line. Given the demand distribution parameters of vertical scaling (a), geographical offset (b), and baseline activity level (c), determine this critical boundary line that helps optimize driver positioning across the service area.
    

    """
def parabola_directrix(a, b, c):
    """
    Calculate the horizontal line (directrix) in the city's coordinate system where the ratio of distance between any point on the ride-sharing demand curve and a central focal point equals the distance from that same point to this line. Given the demand distribution parameters of vertical scaling (a), geographical offset (b), and baseline activity level (c), determine this critical boundary line that helps optimize driver positioning across the service area.
    

    """
    directrix = int(c - (b * b + 1) * 4 * a)
    return directrix