OG详解-OG1 数学2 Q23

Choice B is correct. The standard form of an equation of a circle in the xy-plane is (x -h)²+ (y -k)² = r² , 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  r²= 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.