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Choice C is correct. It’s given that in the xy-plane, the graph of the given equation is a circle. The equation of a circle in the xy-plane can be written - 2+ - 2= 2 in the form ^x hh ^y kh r , where ^h,kh is the center of the circle and r is the length of the circle’s radius. Subtracting 6y from both sides 2+14 + 2=6 +109 2+14 + 2-6 =109 of the equation x x y y yields x x y y . By completing the square, this equation can be rewritten as 2+14 + 14 2 + 2-6 + -6 2 =109+ 14 2 + -6 2 ax x ` 2 j k ay y ` 2 j k ` 2 j ` 2 j . This equation 45 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 2+14 +49 + 2-6 +9 =109+49+9 can be rewritten as ^x x h ^y y h , or +7 2+ -3 2=167 2=167 ^x h ^y h . Therefore, r . Taking the square root of both = 167 =- 167 sides of this equation yields r and r . Since r is the length of the circle’s radius, r must be positive. Therefore, the length of the circle’s 167 radius is . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.