A straight portion of a railway runs due east and is followed by a further straight that runs N15E, the straights being joined by a circular curve of radius 1800 m. In an improvement scheme it is decided to introduce at each end of a circular curve a transition (cubic parabola) 150 m long in such a manner that the route length remains the same.
Calculate
(a) the distance of the new tangent points from the intersection points;
(b) the amount by which the 'halfway' point of the curve has to be moved.