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.

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