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 .