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Analytical Geometry by P. R. Vittal

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Chapter 2

The Straight Line

2.1  INTRODUCTION

In the previous chapter, we defined that the locus of a point is the path traced out by a moving point according to some geometrical law. We know that the locus of a point which moves in such a way that its distance from a fixed point is always constant.

2.1.1  Determination of the General Equation of a Straight Line

Suppose the point P(x, y) moves such that P(x, y), A(4, −1), and B(2, 3) form a straight line. Then, equation

 

x(−4) − y(2) + 14 = 0

 

(i.e.) 4x + 2y − 14 = 0 or 2x + y − 7 = 0, which is a first degree equation in x and y that represents a straight line.

The general equation of a straight line ...

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