Normal form of the line x+y+2=0 is

x+y+2=0 ⇒x+y=−2 ⇒x(−12)+y(−12)=1 ⇒xcos5π4+ysin5π4=1

Normal form of the line x+y+2=0 is

x+y+2=0 ⇒x+y=−2 ⇒x(−12)+y(−12)=1 ⇒xcos5π4+ysin5π4=1

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Normal form of the line $x + y + \sqrt{2} = 0$ is

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$x \cos \frac{7 π}{4} + y \sin \frac{7 π}{4} = 1$

$x \cos \frac{π}{4} + y \sin \frac{π}{4} = 1$

$x \cos \frac{3 π}{4} + y \sin \frac{3 π}{4} = 1$

$x \cos \frac{5 π}{4} + y \sin \frac{5 π}{4} = 1$

answer is C.

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Detailed Solution

$x + y + \sqrt{2} = 0$

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

$\Rightarrow x (\frac{- 1}{\sqrt{2}}) + y (\frac{- 1}{\sqrt{2}}) = 1$

$\Rightarrow x \cos \frac{5 π}{4} + y \sin \frac{5 π}{4} = 1$

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Normal form of the line x+y+2=0 is

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Normal form of the line $x + y + \sqrt{2} = 0$ is