(x+4)^2 +(y−19)^2 = 121 The graph of the given equation is a circle in the xy-plane. The point (a,b) lies on the circle. Which of the following is a possible value for a?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
- 2+ - 2= 2 Choice B is correct. An equation of the form ^x hh ^y kh r , where h, k, and r are constants, represents a circle in the xy-plane with center ^h,kh and radius r. Therefore, the circle represented by the given equation has center -4,19 - ^ h and radius 11. Since the center of the circle has an x-coordinate of 4 and the radius of the circle is 11, the least possible x-coordinate for any point on -4-11 -15 the circle is , or . Similarly, the greatest possible x-coordinate for any -4+11 point on the circle is , or 7. Therefore, if the point ^a,bh lies on the circle, it -15# #7 -14 must be true that a . Of the given choices, only satisfies this inequality. 39 SAT PRACTICE TEST #5 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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