Question

Reduce the following equation to the normal form and find p and α in x − 3 = 0.

Answer 1

x − 3 = 0

\[\Rightarrow x = 3\]

\[ \Rightarrow x + 0 \times y = 3\]

\[ \Rightarrow \frac{x}{\sqrt{1^2 + 0^2}} + 0 \times \frac{y}{\sqrt{1^2 + 0^2}} = \frac{3}{\sqrt{1^2 + 0^2}} \left[\text {  Dividing both sides by }\sqrt{\left( \text { coefficient of x } \right)^2 + \left( \text { coefficient of y } \right)^2} \right]\]

\[ \Rightarrow x + 0 \times y = 3\]

This is the normal form of the given line, where p = 3,

\[cos\alpha = 1\] and \[\text { sin }\alpha = 0 \Rightarrow \alpha = 0\].