If is the length of perpendicular from origin to the non-vertical line and is the inclination of , then show that the equation of the line is
To prove this equation of straight in normal form, Let be any point on the straight line . Since the line intersects the coordinate axes at points and , so and becomes its X-intercept and Y-intercept as shown in the given diagram. Now using equation of straight line intercepts form, we have
If is the foot of the perpendicular draw from origin to the non-vertical straight line, then consider is the right triangle as given in the diagram, so using the trigonometric ratio as follows
Since is a right triangle, so
Now the putting the values of and in equation (i), we get
Which is the equation of straight line in normal form.