(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 ?

Question

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 ≤ a ≤ 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.

Want a deeper, personalized explanation?

Related questions