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Analytical Geometry by P. R. Vittal

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Chapter 10

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 OX and OY parallel to Ox and Oy, respectively. ...

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