10.5 Notes - Rotation of Axes At times we may be faced with an equation of a conic section whose axes would not be parallel to the x or y-axes. (These conics have an equation of the form where .) As a result it may be difficult to ascertain the nature of the graph or its position on the coordinate system. In this case we may simplify the equation by a process of rotating the axes. ? In the figure the axes have been rotated through an acute angle about the origin to produce a new pair of axes, which we will call the X and Y axes. A point P that has coordinates (x, y) in the old system has coordinates (X,Y) in the new system. Let r equal the distance of P from the origin. Let be the angle that segment OP makes with the X axis. ? ?