The normal form of the line x+y+2=0 is

x cos 3 π 4 + y sin 3 π 4 = 1

x cos 3 π 4 + y sin 3 π 4 = 1

x cos 5 π 4 + y sin 5 π 4 = 1

x cos 3 π 4 + y sin 3 π 4 = 1

x cos 7 π 4 + y sin 7 π 4 = 1

Book Online Demo

Check Your IQ

Try Test

Courses

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

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

x \cos \frac{5 π}{4} + y \sin \frac{5 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{7 π}{4} + y \sin \frac{7 π}{4} = 1

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

x + y + \sqrt{2} = 0

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

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

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

Compare with $x \cos α + y \sin α = P$

$\cos α = \frac{- 1}{\sqrt{2}}$ , $\sin α = \frac{- 1}{\sqrt{2}}$

sin and cos are –ve in 3^rd quadrant.

$\cos α = \cos (180 ° + 45 °) = \cos 225 °$

$\cos α = \cos \frac{5 π}{4}$

$α = \frac{5 π}{4}$

$∴$ The normal form of $x + y + \sqrt{2} = 0$ is $x \cos \frac{5 π}{4} + y \sin \frac{5 π}{4} = 1$

Watch 3-min video & get full concept clarity