Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x- axis.(i) x - y+ 8 = 0 (ii) y – 2 = 0 (iii) x – y = 4

-x + = 8

Now a = 1, b =

Here = = = 2

Thus, =

or = 4

x cos 120⁰ + y sin 120⁰ = 4 (normal form)

Where p = 4 and ω = 120⁰

(ii) y – 2 = 0

y = 2

Now a = 0, b = 1

Here, = = 1

Thus, Ox + 1y = 2

or x cos 90⁰ + y sin 90⁰ = 2 (normal form)

where ω = 90⁰ and p = 2

(iii) x – y = 4

Now a = 1, b = -1

Here, = =

Thus = 4

or x cos 315⁹ + y sin(315⁰) = 4 (normal form)

where ω = 315⁰ and p = 4.