Identify the type of graph.
-$( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + 11 = 0$
A) The graph is an ellipse with center (6, -3).
B) The graph is the point (-6, 3).
C) The graph is a circle with center (-6, 3).
D) The equation has no graph.

Question

Quizplus · Accepted Answer

The equation given is of the form $(x - h)^2 + (y - k)^2 = r^2$, which typically represents a circle with center $(h, k)$ and radius $r$. However, in this case, the right side of the equation is negative ($11 = 0$), which is impossible for a circle's equation since the radius squared ($r^2$) cannot be negative. Therefore, this equation does not represent a graphable figure in real number coordinates.

Identify the Type of Graph (x+6)2+(y−3)2+11=0( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + 11 = 0(x+6)2+(y−3)2+11=0

Identify the Type of Graph $( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + 11 = 0$