Question

Find the equation of the line at a distance of:
$\sqrt{2}$ units form the origin and having inclination ${135}^o$

Answer 1

Equation of a line in the normal form is given by

$x\cos \alpha +y\sin \alpha =d$ ; $d$ is the perpendicular distance from the origin

$\therefore$ $x{\cos 45}^0+y{\sin 45}^0=\sqrt{2}$

$\Rightarrow \frac{x}{\sqrt{2}}+\frac{y}{\sqrt{2}}=\sqrt{2}$

$\Rightarrow x+y=2$