Question

Find the equation of a line for p = 8, α = 225°.

Answer 1

Here, p = 8, α = 225°
So, the equation of the line in normal form is

\[x\cos {225}^\circ + y\sin {225}^\circ = 8\]

\[ \Rightarrow x\cos\left( {180}^\circ + {45}^\circ \right) + y\sin\left( {180}^\circ + {45}^\circ \right) = 8\]

\[ \Rightarrow - x\cos {45}^\circ - y\sin {45}^\circ = 8\]

\[ \Rightarrow - \frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}} = 8\]

\[ \Rightarrow x + y + 8\sqrt{2} = 0\]