110. Write the normal equation of the line if the length of the normal $p=3$, and the angle $\alpha$, formed by it with the positive direction of the $O x$ axis, is $45^{\circ} ; 315^{\circ}$.
Solution. We will use formula (2). According to the condition: 1) $p=3, \alpha=45^{\circ}$, therefore, $x \cdot \cos 45^{\circ}+y \cdot \sin 45^{\circ}-3=0$

or

$$
\frac{\sqrt{2}}{2} x+\frac{\sqrt{2}}{2} y-3=0
$$

2) $p=3, \alpha=315^{\circ}$, therefore,

$$
x \cdot \cos 315^{\circ}+y \cdot \sin 315^{\circ}-3=0
$$

or

$$
\frac{\sqrt{2}}{2} x-\frac{\sqrt{2}}{2} y-3=0
$$