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Question
Find the equations of the bisectors of the angles between the coordinate axes.
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Solution
There are two bisectors of the coordinate axes.
Their inclinations with the positive x-axis are
\[{45}^\circ \text { and } {135}^\circ\]
So, the slope of the bisector is \[m = \tan {45}^\circ \text { or } m = \tan {135}^\circ , \text { i . e . m = 1 or } m = - 1\] and c = 0.
Substituting the values of m and c in y = mx + c, we get,
y = x + 0
\[\Rightarrow\] x \[-\] y = 0 or y = - x + 0
\[\Rightarrow\] x + y = 0
Hence, the equation of the bisector is \[x \pm y = 0\].
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