Final answer:
The polar equation for the curve x² + y² = 49 is r = 7.
Step-by-step explanation:
To find a polar equation for the curve represented by the Cartesian equation x² + y² = 49, we can convert the equation from Cartesian coordinates (x, y) to polar coordinates (r, θ). In polar coordinates, x = r cos(θ) and y = r sin(θ). Substituting these expressions into the Cartesian equation, we get r² cos²(θ) + r² sin²(θ) = 49. Simplifying this equation, we have r² = 49. Therefore, the polar equation for the curve is r = 7, where r represents the distance from the origin to a point on the curve and θ represents the angle that the radius vector to the point makes with the positive x-axis.