Question

Reduce the equation $x-y=4$ into normal form. Find their perpendicular distance from the origin and angle between perpendicular and the positive x-axis

Answer 1

Solution -

$x-y=4$

$\frac{x}{4}-\frac{y}{4}=1$ Normal Form

Distance from origin $=\left|\frac{-4}{\sqrt{1+1}}\right|=2\sqrt{2}$

Angle with positive x-axis $=ta{n}^{-1}\left(\frac{4}{4}\right)={45}^{\circ }$

Angle with $\perp$ positive x-axis $={90}^{\circ }-{45}^{\circ }={45}^{\circ }$