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Introduction

While studying co-ordinate
geometry (aka analytic geometry) in intermediate classes we normally
arrive at the study of conic sections or in short "conics". Three new
curves namely "ellipse", "parabola", and "hyperbola" come into picture
and their theory is quite unlike those of the elementary geometrical
objects (line, triangle, circle etc) studied in secondary classes. In
case of the elementary geometrical objects like points, lines,
triangles, circles we have two approaches: 1) using the axioms of Euclid
and then deducing the properties of these objects logically from
Euclid's axioms and, 2) using the language of coordinate geometry which
transforms the subject of geometry into algebra. Unfortunately the
beautiful approach of using Euclid's axioms is discarded in higher
secondary classes in favor of the approach using coordinate geometry
which makes the subject dull with huge amount of laborious algebraical
manipulations. In fact most students think that the only way to study
new curves like ellipses, parabola and hyperbola is through coordinate
geometry.