Find an equation equivalent to 2x + 3y = 6 in polar coordinates.

Solution:

To find the equivalent in polar coordinates we consider the figure given below:

The equation 2x + 3y = 6 can be written in polar coordinates as:

2(rcosθ) + 3 (rsinθ) = 6

Taking r(radius of the circle or the radius vector) common we have

r(2cosθ + 3sinθ) = 6

r = 6/(2cosθ + 3sinθ)

Find an equation equivalent to 2x + 3y = 6 in polar coordinates.

Summary:

The equation equivalent to 2x + 3y = 6 in polar coordinates is r = 6/(2cosθ + 3sinθ)