Question

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

a. r (2 sin e + 3 cos a) = 6
b. 2 cose - 3 sin e = 6r
c. 7 (2 cose + 3 sin ) = 6
d. 2 sin e + 3 cose = 6r

Answer 1

By substituting the polar coordinate expressions for x and y into the original Cartesian equation, the equivalent polar coordinate equation is found to be r(2 × cos(θ) + 3 × sin(θ)) = 6.

Step-by-step explanation:

To find an equation equivalent to 2x + 3y = 6 in polar coordinates, we use the relationships x = r × cos(θ) and y = r × sin(θ). Substituting these into the original equation, we get 2(r × cos(θ)) + 3(r × sin(θ)) = 6. Simplifying, we obtain 2r × cos(θ) + 3r × sin(θ) = 6 or r(2 × cos(θ) + 3 × sin(θ)) = 6. Therefore, the equivalent equation in polar coordinates is r(2 × cos(θ) + 3 × sin(θ)) = 6, which corresponds to option a in the given choices.