x + 4 2 + y - 19 2 = 121 The graph of the given equation is a circle

Question

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 ?

Accepted Answer

Choice B is correct. An equation of the form x - h 2 + y - k 2 = r 2 , where h , k , and r are constants, represents a circle in the xy -plane with center h , k and radius r . Therefore, the circle represented by the given equation has center - 4 , 19 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 the circle is - 4 - 11 , or - 15 . Similarly, the greatest possible x -coordinate for any point on the circle is - 4 + 11 , or 7 . Therefore, if the point a , b lies on the circle, it must be true that - 15 &#8804; a &#8804; 7 . Of the given choices, only - 14 satisfies this inequality. 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.

Question x-4-2-