Question -
Answer -
(i) p = 5, α = 60°
Given:
p = 5, α = 60°
The equation of theline in normal form is given by
Using the formula,
x cos α + y sin α= p
Now, substitute thevalues, we get
x cos 60° + y sin 60°= 5
x/2 + √3y/2 = 5
x + √3y = 10
∴ The equation of linein normal form is x + √3y = 10.
(ii) p = 4, α = 150°
Given:
p = 4, α = 150°
The equation of theline in normal form is given by
Using the formula,
x cos α + y sin α= p
Now, substitute thevalues, we get
x cos 150° + y sin150° = 4
cos (180° – θ) =– cos θ , sin (180° – θ) = sin θ
x cos(180° – 30°)+ y sin(180° – 30°) = 4
– x cos 30° + ysin 30° = 4
–√3x/2 + y/2 = 4
-√3x + y = 8
∴ The equation of linein normal form is -√3x + y= 8.