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.
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:
The roots of this equation must be the gradients of the lines m and t.
Therefore and .
Angles Between Lines
Suppose that lines y = mx and y = tx are represented by the following equation:
If the angle between them is θ then:
Hence
Therefore,
N. B. The lines will be parallel if the values of this fraction become infinite, i.e. a+b=0.
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