OG详解-OG7 数学1 Q35

Choice A is correct. For a circle in the xy-plane that has the equation (x-h)² +(y-k)² = r², where h, k, and r are constants, (h, k) is the center of the circle and the positive value of r is the radius of the circle. In the given equation,  h = 13 and r² = 64. Taking the square root of each side of r² = 64 yields r = ±8.  Therefore, the center of the circle is at (13, k) and the radius is 8.
Choice B is incorrect. This gives the center and radius of a circle with equation  (x-k)² +(y-13)² = 64, not (x-13)² +(y-k)² = 64. Choice C is incorrect. This gives the center and radius of a circle with equation (x-k)² +(y-13)² = 4,096, not (x-13)² +(y-k)² = 64. Choice D is incorrect. This gives the center and radius of a circle with equation (x-13)² +(y-k)² = 4,096, not (x-13)² +(y-k)² = 64.