Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality?
$$( x + 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } 16$$
A) The region inside the circle with center $( 6 , - 6 )$ and radius 4
B) The region outside a circle with center $( 6 , - 6 )$ and radius 4
C) The region outside a circle with center $( - 6,6 )$ and radius 4
D) The region inside a circle with center $( - 6,6 )$ and radius 4

Question

Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality?
$$( x + 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } > 16$$
A) The region inside the circle with center $( 6 , - 6 )$ and radius 4
B) The region outside a circle with center $( 6 , - 6 )$ and radius 4
C) The region outside a circle with center $( - 6,6 )$ and radius 4
D) The region inside a circle with center $( - 6,6 )$ and radius 4

Quizplus · Accepted Answer

The equation resembles the standard form of a circle $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. However, the inequality sign ">" indicates the region outside the circle. The correct center is $(-6, 6)$ and the radius is $\sqrt{16} = 4$, making option C correct.

Provide an Appropriate Response (x+6)2+(y−6)2>16( x + 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } > 16(x+6)2+(y−6)2>16

Provide an Appropriate Response $( x + 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } > 16$