What is the diameter of the circle in the xy-plane with equation (x − 5) 2 + (y − 3) 2 = 16?

Question

Accepted Answer

Choice B is correct. The standard form of an equation of a circle in the xy-plane is (x − h) 2 + (y − k) 2 = r 2 , where the coordinates of the center of the circle are (h, k) and the length of the radius of the circle is r. For the circle in the xy-plane with equation (x − 5) 2 + (y − 3) 2 = 16, it follows that r 2 = 16. Taking the square root of both sides of this equation yields r = 4 or r = −4. Because r represents the length of the radius of the circle and this length must be positive, r = 4. Therefore, the radius of the circle is 4. The diameter of a circle is twice the length of the radius of the circle. Thus, 2(4) yields 8. Therefore, the diameter of the circle is 8. Choice A is incorrect. This is the radius of the circle. Choice C is incorrect. This is the square of the radius of the circle. Choice D is incorrect and may result from conceptual or calculation errors.

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