# 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

(i) x - y + 8 = 0

-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.

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