Question

Reduce the following equation to the normal form and find p and α in y − 2 = 0.

Answer 1

y − 2 = 0

\[\Rightarrow y = 2\]

\[ \Rightarrow 0 \times x + y = 2\]

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

\[ \Rightarrow 0 \times x + y = 2\]

This is the normal form of the given line, where p = 2,

\[\text { cos }\alpha = 0\] and \[\text { sin }\alpha = 1 \Rightarrow \alpha = {90}^\circ\].