Question

Which of the following polar equations describes a circle centered at {3}{2}, 1 )) with radius (frac sqrt{13}}{2}) ?

(A) ( r=2 sin )
B) ( r=2 cos +3")

Answer 1

The polar equation of a circle centered at (3/2, 1) with radius √(13)/2 would be in the form of either r = 2√(13)/2 cos(θ - π/2) or r = 2√(13)/2 sin(θ - 3π/2), but neither given option A or B is correct.

Step-by-step explanation:

The student's question is related to finding the polar equation of a circle with a given center and radius. When dealing with polar coordinates, a circle centered at the pole (r, θ) can be described with the equation r = 2α cos(θ - φ) or r = 2α sin(θ - φ), where α is the radius of the circle and φ is the angle that locates the center of the circle.

Given the circle's center is at (3/2, 1) and the radius is √(13)/2, the equation to use in this case would be r = 2√(13)/2 cos(θ - π/2) or r = 2√(13)/2 sin(θ - 3π/2), depending on the orientation of the circle in the pole. However, neither (A) r=2 sin or (B) r=2 cos +3" correspond to the correct equation of a circle centered at (3/2, 1) with radius √(13)/2 in polar coordinates.