Analytical Geometry

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:

Also consider the 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, ...