Equation of line in Straight lines

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Question

If a and b are slopes of the angular bisectors of the coordinate axes then $a^{2} + b^{2}$ is

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Solution

The angular bisectors of coordinate axes are $x + y = 0$ and $x - y = 0$
Slopes are $a = - 1, b = 1$
It implies that
$\begin{matrix} a^{2} + b^{2} = 1^{2} + {(- 1)}^{2} \\ = 1 + 1 \\ = 2 \end{matrix}$
Therefore, $a^{2} + b^{2} = 2$

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