Intercept Form
If a line L makes x-intercept a and y-intercept b on the axes, that is L meets x-axis at the point( a, 0) and y-axis at the point, then equation of the line is x / a + y / b = 1
Numerical: Find the equation of the line, which makes intercepts – 3 and 2 on x- and y-axes respectively.
Solution: Here a = – 3 and b = 2. By using the formaul is x / a + y / b = 1, we get
x /-3 + y / 2 = 1 or 2x-3y + 6 = 0
Normal Form
Suppose a non-vertical line is known to us with following data:( i) Length of the perpendicular( normal) from origin to the line.( ii) Angle which normal makes with the positive direction of x-axis
Then the equation of the line will be x cos ω + y sin ω = p, where p is the length of perpendicular & ω is the angle perpendicular makes with positive x axis.