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Question
Reduce the following equation to the normal form and find p and α in x − 3 = 0.
Solution
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 \[\text { sin }\alpha = 0 \Rightarrow \alpha = 0\].
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