A circle in the xy -plane has the equation ( x - 13 ) 2 + ( y - k

Question

A circle in the xy -plane has the equation ( x - 13 ) 2 + ( y - k ) 2 = 64 . Which of the following gives the center of the circle and its radius?

Accepted Answer

Choice A is correct. For a circle in the xy -plane that has the equation x - h 2 + y - k 2 = r 2 , 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 r 2 = 64 . Taking the square root of each side of r 2 = 64 yields r = &plusmn; 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 .

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