Identify the type of graph.
-$$\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 0$$
A) The graph is the point $( 8,4 )$.
B) The graph is an ellipse with center at $( - 8 , - 4 )$.
C) The graph is a hyperbola opening right and left.
D) The graph is an ellipse with center at $( 8,4 )$.

Question

Quizplus · Accepted Answer

The equation is of the form $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 0$, where $a^2$ and $b^2$ are positive. However, since the sum of two squares equals zero, both squares must be zero, indicating the graph is a single point at $(h, k)$, which is $(8, 4)$.

Identify the Type of Graph (x−8)25+(y−4)29=0\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 05(x−8)2​+9(y−4)2​=0

Identify the Type of Graph $\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 0$