Match each item with the correct graph to obtain a true statement.
-$\phi$
A) $x ^ { 2 } + 2 y ^ { 2 } = 0$
B) $x ^ { 2 } + 2 y ^ { 2 } = 16$
C) $x ^ { 2 } + 2 y ^ { 2 } = - 16$

Question

Match each item with the correct graph to obtain a true statement.
-$\phi$ 
A) $x ^ { 2 } + 2 y ^ { 2 } = 0$ 
B) $x ^ { 2 } + 2 y ^ { 2 } = 16$ 
C) $x ^ { 2 } + 2 y ^ { 2 } = - 16$

Quizplus · Accepted Answer

The equation $x ^ { 2 } + 2 y ^ { 2 } = - 16$ has no real solutions, as adding non-negative values (squares of x and 2y) can never result in a negative number. Therefore, the graph for this equation does not exist. The other two graphs do exist and can be seen in the following images:

Graph A:

Graph B:

Neither of these graphs contain any real points where $x ^ { 2 } + 2 y ^ { 2 } = 0$, so neither match with $\phi$ (which could represent a solution to the equation). Therefore, the only possible match is with the non-existent graph C.

Match Each Item with the Correct Graph to Obtain a True