A line makes an angle 450 with X-axis and at a distance of 2 from the origin. Its equation is

m=1Normal makes an angle with x-axis is135odistance from origin =2The equation of Normal is x cosα+y sinα=pxcos135o+ysin135o=2 -x2+y2=2⇒y-x=2

A line makes an angle 450 with X-axis and at a distance of 2 from the origin. Its equation is

m=1Normal makes an angle with x-axis is135odistance from origin =2The equation of Normal is x cosα+y sinα=pxcos135o+ysin135o=2 -x2+y2=2⇒y-x=2

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A line makes an angle $45^{0}$ with X-axis and at a distance of $\sqrt{2}$ from the origin. Its equation is

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$\sqrt{2} x + y = 1$

$x + y \sqrt{2} = 1$

$y - x = \sqrt{2}$

$y - x = 2$

answer is C.

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Detailed Solution

m=1
Normal makes an angle with x-axis is $135^{o}$
distance from origin $= \sqrt{2}$
The equation of Normal is $x \cos α + y \sin α = p$
$x \cos 135^{o} + y \sin 135^{o} = \sqrt{2} - \frac{x}{2} + \frac{y}{\sqrt{2}} = \sqrt{2} \Rightarrow y - x = 2$