How to Find the Polar Equation of A Line?

Polar coordinate system is used to define the two dimensional coordinate system which is very familiar to Cartesian coordinate system. We can convert the equation of line into polar form. Now let us see how to find the polar equation of a line.
In the Cartesian coordinate system we assume origin points as (0, 0). Basically the polar form is described by two factors:

1. Radial distance: This is the distance from origin to a particular Point which is represented by the variable ‘r’.

2. Angle: This is represented by θ which is formed by the arbitrary axis.
Now let us see the procedure to convert the line equation into polar equation.

Step 1: First of all we require equation of line which should be in the form of y = mx + c. Here (x, y) are coordinates of the line, 'm' is the Slope of line and 'c' is the y- intercept. Assume that we have an equation 3x = y + 5. Now we will convert it in the standard form like:
y = 3x – 5.

Step 2: Now we will replace y- coordinates with r sin θ. So above equation will be changed as
r sinθ = 3x - 5.

Step 3: Now change the x- coordinates in polar form as well. So we will replace x- coordinates with r cos θ. Now the equation will be changed into r sinθ = 3r cos θ – 5.

Step 4: Now whole equation is in the form of 'r' and 'θ'. So we can say that this is a polar equation of line. Now we will write it in the terms of 'r' as:
r = 5 / (3 cosθ - sinθ).