Final answer:
The question asks for a polar equation of a circle centered at (3, 3/2) with a radius of 3√5/2. The polar equation can be found by converting the center's Cartesian coordinates to polar coordinates and using the formula for a circle in polar coordinates.
Step-by-step explanation:
The student's question is about finding the polar equation that describes a circle. To write the equation of a circle in polar coordinates, we use the formula r = √((x - h)^2 + (y - k)^2), where (h, k) is the center of the circle. For a circle centered at (3, 3/2) with a radius of 3√5/2, we need to apply the conversion from Cartesian coordinates to polar coordinates. Firstly, let's recall that Cartesian coordinates (x, y) are related to polar coordinates (r, θ) by the equations x = rcos(θ) and y = rsin(θ). Therefore, the given center of the circle (3, 3/2) needs to be represented in polar coordinates. After getting the polar form of the center, the radius is already given as 3√5/2. The final step is to combine these values into the general formula to obtain the polar equation of the circle.