Tracing of Curves
10.1 GENERAL EQUATION OF THE SECOND DEGREE AND TRACING of a CONIC
In the earlier chapters, we studied standard forms of a conic namely a parabola, ellipse and hyperbola. In this chapter, we study the conditions for the general equation of the second degree to represent the different types of conic. In order to study these properties, we introduce the characteristics of change of origin and the coordinate axes, rotation of axes without changing the origin and reducing the second degree equation without xy-term.
10.2 SHIFT OF ORIGIN WITHOUT CHANGING THE DIRECTION OF AXES
Let Ox and Oy be two perpendicular lines on a plane. Let O′ be a point in the xy-plane. Through O′, draw O′X and O′Y parallel to Ox and Oy, respectively. ...