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A circle in the xy-plane has the equation x−13 + y−k = 64 ()^2 ()^2. Which of the following gives the center of the circle and its radius? (13,k)
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice A is correct. For a circle in the xy-plane that has the equation - 2+ - 2= 2 ^x hh ^y kh r , where h, k, and r are constants, ^h,kh is the center of the circle and the positive value of r is the radius of the circle. In the given equation, =13 2=64 2=64 =! h and r . Taking the square root of each side of r yields r 8. 13, Therefore, the center of the circle is at ^ kh and the radius is 8. Choice B is incorrect. This gives the center and radius of a circle with equation - 2+ -13 2=64 -13 2+ - 2=64 ^x kh ^y h , not ^x h ^y kh . Choice C is incorrect. This - 2+ -13 2=4,096 gives the center and radius of a circle with equation ^x kh ^y h , -13 2+ - 2=64 not ^x h ^y kh . Choice D is incorrect. This gives the center and -13 2+ - 2=4,096 radius of a circle with equation ^x h ^y kh , not -13 2+ - 2=64 ^x h ^y kh . 34 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1
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