Find the equation of the line for which
Question:

Find the equation of the line for which

p = 3 and ∝ = 450

Solution:

To Find:The equation of the line.

Given: $p=3$ and $\propto=450$

Here $p$ is the perpendicular that makes an angle $\propto$ with positive direction of $x$-axis, hence the equation of the straight line is given by:

Formula used:

$x \cos \alpha+y \sin \alpha=p$

$x \cos 450+y \sin 450=3$

i.e; $\cos 450=\cos (360+90)=\cos 90[\because \cos (360+x)=\cos x]$

similarly, $\sin 450=\sin (360+90)=\sin 90[\because \sin (360+x)=\sin x]$

hence, $x \cos 90+y \sin 90=3$

$x \times(0)+y \times 1=3$

Hence the required equation of the line is y=3.