Lesson 7.6
The normal form of a linear equation is
where p is the length of the normal from the
line to the origin and is the positive angle
formed by the positive x-axis and the normal.
Example 1
Write the standard form of the equation of a line for which
the length of the normal segment to the origin is 8
and the normal makes an angle of 135° with the positive
x-axis.
Normal form
 = 135° and p = 8
=0
=0
Multiply each side by -2.
=0
Divide each side by -
=0
.
The standard form of a linear equation,
Ax + By + C = 0,
can be changed to normal form by dividing
each term by
The sign is chosen opposite the sign of C
Example 2
Write each equation in normal form. Then find the length of the
normal and the angle it makes with the x-axis.
a.
5x + 4y - 12 = 0