Graphical Interpretation of Difficult Curves: Identifying Curves such as the Circle, Ellipse, Hyperbola and Parabola and Reducing to a Single Drawing

VERY often in technical work we meet with a curve of the type, 8x2 + 12xy + 17y2—28x −46y + 17=0. It may occur in the solution of problems in structures, aerodynamics, performance, etc. At first sight a curve of this nature looks quite complicated, but in actual fact it is only an ellipse x2/4 + y2/1 = 1 which has been moved bodily and then rotated.