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 $45^{\circ} and 135^{\circ}$ .
So, the slope of the bisector is $m = \tan 45^{\circ} or m = \tan 135^{\circ}, i . e . m = 1 or m = - 1$ 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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