What is the diameter of the circle in the xy -plane with equation x - 5 2 + y -

Question

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

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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