LOCUS VARIOUS FORMS OF LINES

LOCUS VARIOUS FORMS OF LINES
Normal form (or) Perpendicular form

The equation of the line in normal form is \(x\cos \alpha + y\sin \alpha = p\)
Where p = The perpendicular distance from the origin to the line
\(\alpha \)=The angle made by the perpendicular line, with x-axis in the positive direction.
NOTE:   Bounds of  p and  \(\alpha \),
    here \(p \geqslant 0\) and  \(0 \leqslant \alpha < {360^0}\)
Symmetric form: 
    The equation  of the line passing through the point \((x_1,y_1)\)  and making an  angle \(\theta\) with x-axis in the positive direction is
     \(\frac{{x - {x_1}}}{{\cos \theta }} = \frac{{y - {y_1}}}{{\sin \theta }}\) where \(\theta \in R - \){(2n+1)\(\pi \over 2\) and \(n\pi\),\(n\in Z\)}