Given equation of straight line be ax+by+c=0
A line parallel to given line is ax+by+d=0 only constant term changes.
A line perpendicular to given line is bx-ay+k=0
Here change coordinate of x as coordinate of y & coordinate of y as negative of coordinate of x and constant term changes
It the lines a1 x+b1 y+c1 = 0 and a2 x+b2 y+c2 = 0 are prependecular then a1 a2 +b1 b2 = 0
i. Coincident, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
ii. Parallel, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}\)
iii. Intersecting, if \(\frac{a_1}{a_2}≠\frac{b_1}{b_2}\)
