To convert the Cartesian equation x² + y² = 6cx into polar coordinates, we need to use the relationships between Cartesian and polar coordinates:
- x = r cos(θ)
- y = r sin(θ)
- x² + y² = r²
Substituting x and y in terms of r and θ into the original equation:
x² + y² = 6cx
We can express this as:
r² = 6c(r imes cos(θ))
Next, we can simplify this equation:
Dividing both sides by r (assuming r ≠ 0):
r = 6c cos(θ)
This gives us the polar equation of the curve represented by the original Cartesian equation. Thus, the polar form is:
r = 6c cos(θ)
This describes a circle in polar coordinates centered along the x-axis, depending on the value of c.