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).