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  Pair of Straight Lines Homework Help - K-12 Grade Level, College Level Mathematics

Introduction of Pair of Straight Line

Any two lines through the Origin may be written as y = mx and y=tx where m and t are their gradients. So, (y - mx)(y - tx) = 0 giving y -mx  or y - tx = 0 must represent the pair.

2201_Pair of Straight Line Homework Help 6.jpg

General form of this equation is:

ax2 + 2hxy + by2 = 0

This equation must represent a pair of straight lines, imaginary or real, through the origin.

Can be written as:

1023_Pair of Straight Line Homework Help.jpg

The roots of this equation must be the gradients of the lines m and t.

Therefore 35_Pair of Straight Line Homework Help 1.jpg and 1499_Pair of Straight Line Homework Help 2.jpg.

Angles Between Lines

Suppose that lines y = mx and y = tx are represented by the following equation:

ax2 + 2hxy + by2 = 0

If the angle between them is θ then:

68_Pair of Straight Line Homework Help 3.jpg

Hence

1437_Pair of Straight Line Homework Help 4.jpg

Therefore,

937_Pair of Straight Line Homework Help 5.jpg

N. B. The lines will be parallel if the values of this fraction become infinite, i.e. a+b=0.

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