x + 4 2 + y - 19 2 = 121 The graph of the given

Choice B is correct. An equation of the form ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$, where $h$, $k$, and $r$ are constants, represents a circle in the xy-plane with center $\left(h,k\right)$ and radius $r$. Therefore, the circle represented by the given equation has center $\left(-4,19\right)$ 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 $\left(a,b\right)$ lies on the circle, it must be true that $-15\le a\le 7$. 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.