OG详解-OG5 数学1 Q22

Choice B is correct. An equation of the form (x-h)² +(y-k)² = r², 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.