Find a polar equation for the curve represented by the given Cartesian equation. 2x + 3y = 6

Solution:

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

x = rcosθ and y = rsinθ

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)

Summary:

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

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