Question

find the equation of line making an angle of 45° with positive X axis and at a distance 2under root2 from the origin ​

Answer 1

Answer:

x - y + 4 = 0.

Step-by-step explanation:

Given :

Angle making with positive 'x' axis is 45.

Line making angle  ( ω ) = 45 + 90 = 135    [ By exterior angle property ]

Distance from origin P = 2 √ 2 unit .

We have normal form equation :

x cos ω + y sin ω = P

Putting value here we get :

x cos 135 + y sin 135 = 2 √ 2

x cos ( 90 + 45 ) + y sin ( 90 + 45 ) = 2 √ 2

x . - sin 45 + y cos 45 = 2 √ 2

- x / √ 2 + y √ 2 = 2 √ 2

Multiply whole equation by √ 2 :

- x + y = 4

x - y + 4 = 0

Therefore , the equation of line is x - y + 4 = 0.

Answer 2

Answer:

y= mx+c

y = tan45+ √2

y= x+√2

y-x= √2