Find the equations of the bisectors of the angles between the coordinate axes.

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Solution

$Then inclinations with the positive x-axis are 45^{\circ} a n d 135^{\circ} . So, the slope of the bisector is m = tan 45^{\circ} o r m = t a n 135^{\circ}, i . e ., m = 1 o r m = - 1 a n d c = 0 Substituting the values of m and c in y = mx + c, we get, y = x + 0 \Rightarrow x - y = 0 o r y = - x + 0 \Rightarrow x + y = 0 Hence, the equation of the bisector is x \pm y = 0.$

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