Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality?
$$( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 }

Question

Provide an appropriate response.
-Which one of the following is a description of the graph of the inequality?
$$( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16$$
A) The region outside a circle with center $( 1,3 )$ and radius 4
B) The region inside a circle with center $( 1,3 )$ and radius 4
C) The region inside the circle with center $( - 1 , - 3 )$ and radius 4
D) The region outside a circle with center $( - 1 , - 3 )$ and radius 4

Quizplus · Accepted Answer

The inequality describes the region inside a circle because of the "<" sign. The circle has a center at $(1,3)$ and a radius of $4$, as derived from the standard form of a circle equation $(x - h)^2 + (y - k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

Provide an Appropriate Response (x−1)2+(y−3)2<16( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16(x−1)2+(y−3)2<16

Provide an Appropriate Response $( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } < 16$