Identify the type of graph.
-$$10 x ^ { 2 } + 100 x + 10 y ^ { 2 } - 220 y = - 1459$$
A) The graph is a circle with center $( - 5,11 )$.
B) The equation has no graph.
C) The graph is the point $( - 5,11 )$.
D) The graph is a circle with center $( 5 , - 11 )$.

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form of a circle's equation by completing the square for both $x$ and $y$. Rearranging and completing the square gives us $(x+5)^2 + (y-11)^2 = r^2$, where $r$ is the radius of the circle. This shows that the graph is a circle with center $(-5, 11)$.

Identify the Type of Graph 10x2+100x+10y2−220y=−145910 x ^ { 2 } + 100 x + 10 y ^ { 2 } - 220 y = - 145910x2+100x+10y2−220y=−1459

Identify the Type of Graph $10 x ^ { 2 } + 100 x + 10 y ^ { 2 } - 220 y = - 1459$