Final answer:
The equation x² + y² = 6x in cylindrical coordinates is r = 6cos(θ). This is obtained by substituting x and y with their cylindrical counterparts r⋅cos(θ) and r⋅sin(θ), and simplifying.
Step-by-step explanation:
To find an equation in cylindrical coordinates for the rectangular equation x² + y² = 6x, we need to utilize the relationship between rectangular and cylindrical coordinates. In cylindrical coordinates, x is represented by r⋅cos(θ) and y is represented by r⋅sin(θ). Substituting these into the rectangular equation, we get:
(r⋅cos(θ))² + (r⋅sin(θ))² = 6(r⋅cos(θ))
Simplifying, since r² = (r⋅cos(θ))² + (r⋅sin(θ))², the equation becomes:
r² = 6r⋅cos(θ)
To get r isolated on one side, we divide both sides by 6cos(θ), which yields:
r = 6cos(θ)
This is the cylindrical equation corresponding to the given rectangular equation.