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Analytical Geometry by P. R. Vittal

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Chapter 3

Pair of Straight Lines

3.1  INTRODUCTION

We know that every linear equation in x and y represents a straight line. That is Ax + By + C = 0, where A, B and C are constants, represents a straight line. Consider two straight lines represented by the following equations:

equation

Also consider the equation

equation

If (x1, y1) is a point on the straight line given by (3.1) then

 

l1x1 + m1y + n1 = 0

 

This shows that (x1, y1) is also a point on the locus of (3.3). Therefore, every point on the line given by (3.1) is also a point on the locus of (3.3). Similarly, ...

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