Question

Find the equation of the line making and angle of 45° with the positive X-axis and at a distance 2√2 from the origin.

Answer 1

Answer: Angle making with positive 'x' axis is 45. Distance from origin P = 2 √ 2 unit . Therefore , the equation of line is x - y + 4 = 0.

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Answer 2

Answer:

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.