Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality? $$( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 }

Question

Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality? $$( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 81$$
A) The region inside a circle with center $( - 6,3 )$ and radius 9
B) The region outside a circle with center $( 6 , - 3 )$ and radius 9
C) The region inside the circle with center $( 6 , - 3 )$ and radius 9
D) The region outside a circle with center $( - 6,3 )$ and radius 9

Quizplus · Accepted Answer

The inequality $(x + 6)^2 + (y - 3)^2 < 81$ represents the region inside a circle because of the "<" symbol. The center of the circle is at $(-6, 3)$, and the radius is $\sqrt{81} = 9$, matching option A.

Provide an Appropriate Response (x+6)2+(y−3)2<81( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 81(x+6)2+(y−3)2<81

Provide an Appropriate Response $( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 81$