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Home » Find the equations of the bisectors of the angles between the coordinate axes.
Find the equations of the bisectors of the angles between the coordinate axes.
CBSE | Class 11 | Exercise 23.3 | Maths | RD Sharma | Straight Lines
Find the equations of the bisectors of the angles between the coordinate axes.

There are two bisectors of the coordinate axes.

Their inclinations with the positive x-axis are

    \[{{45}^{o}}~and\text{ }{{135}^{o}}\]

The slope of the bisector is

    \[m\text{ }=\text{ }tan\text{ }{{45}^{o}}~or\text{ }m\text{ }=\text{ }tan\text{ }{{135}^{o}}\]

i.e.,

    \[m\text{ }=\text{ }1\text{ }or\text{ }m\text{ }=\text{ }-1,\text{ }c\text{ }=\text{ }0\]

By using the formula,

    \[y\text{ }=\text{ }mx\text{ }+\text{ }c\]

Now, substitute the values of

    \[m\text{ }and\text{ }c\]

we get

    \[y\text{ }=\text{ }x\text{ }+\text{ }0\]

    \[x\text{ }\text{ }y\text{ }=\text{ }0\text{ }or\text{ }y\text{ }=\text{ }-x\text{ }+\text{ }0\]

    \[x\text{ }+\text{ }y\text{ }=\text{ }0\]

∴ The equation of the bisector is

    \[x~\pm ~y\text{ }=\text{ }0\]

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