Question

find the equation of the straight line whose distance from the origin is 4 if the normal ray from the origin to the straight line makes an angle of 135 degrees with the positive direction of the x-axis​

Answer 1

Answer:

The equation of the line is $x-y+4\sqrt{2}=0$

Step-by-step explanation:

The equation of a straight line in normal form is given by

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

Where $\theta$ is the angle that the normal from the origin on the straight line, makes with the positive direction of the x-axis and $p$ is the distance of the normal from the origin at the straight line

Here, given that

$\theta=135^\circ$

$p=4$

Therefore, the equation of the straight line will be

$x\cos135^\circ+y\sin135^\circ=4$

or, $x\cos(180^\circ-45^\circ)+y\sin(180^\circ-45^\circ)=4$

or, $-x\cos45^\circ+y\sin45^\circ=4$

or, $-\frac{x}{\sqrt{2}}+\frac{y}{\sqrt{2}}=4$

or, $-x+y=4\sqrt{2}$

or, $x-y+4\sqrt{2}=0$

Hope this helps.