Reduce the equation \(\sqrt{3}\)x + y = 4 into normal form and find th

1.	Reduce the equation \(\sqrt{3}\)x + y = 4 into normal form and find the values of P and a.
Answer» The given equation is \(\sqrt{3}\)x + y = 4 ⇒ \(\frac {\sqrt{3}x}{\sqrt{{(\sqrt{3})^2+1^2}}}\) + \(\frac {y}{\sqrt{{(\sqrt{3})^2+1^2}}}\) = \(\frac {4}{\sqrt{{(\sqrt{3})^2+1^2}}}\),. A = \(\sqrt{3}\), B = 1, C = – 4 ⇒ \(\frac{\sqrt{3}}{2}\)x + \(\frac{1}{2}\)y = \(\frac{4}{2}\) ⇒ x cos 30° + y sin 30° = 2, is the required equation of line in normal form where P = 2, a = 30°

Reduce the equation \(\sqrt{3}\)x + y = 4 into normal form and find the values of P and a.

Answer»

The given equation is

\(\sqrt{3}\)x + y = 4

⇒ \(\frac {\sqrt{3}x}{\sqrt{{(\sqrt{3})^2+1^2}}}\) + \(\frac {y}{\sqrt{{(\sqrt{3})^2+1^2}}}\) = \(\frac {4}{\sqrt{{(\sqrt{3})^2+1^2}}}\),.

A = \(\sqrt{3}\), B = 1, C = – 4

⇒ \(\frac{\sqrt{3}}{2}\)x + \(\frac{1}{2}\)y = \(\frac{4}{2}\)

⇒ x cos 30° + y sin 30° = 2, is the required equation of line in normal form where P = 2, a = 30°