39.1k views
2 votes
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")

1 Answer

3 votes

Final answer:

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.

User Hyunju
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories