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EQUATION OF A STRAIGHT LINE IN NORMAL FORM

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Definition

A normal to a line is a line segment drawn from a point perpendicular to the given line.

Let p be the length of perpendicular form from the origin to a line, which subtends an anglewith the positive direction of x-axis as shown below:

Let AB be a straight line on coordinate axes. p be the perpendicular distance from the origin to the line at be the angle of perpendicular.

Draw

In ,

The coordinates of point P are .

Slope of OP,

The equation of the line AB:

Therefore, the equation of straight line in normal form is:

Example:

Determine the equation of the line with and the perpendicular distancefrom the origin.

The standard equation of the straight line in the normal is:

,

Substitute the known values as follows:

Question 1:

Determine the equation of the line whose perpendicular distance from the origin is 8 units and makes an angle of 90o in positive direction of x-axis.

Solution 1:

The standard equation of the straight line in the normal is:

,

Substitute the known values as follows:

The required equation of a straight line is.

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