Determine Whether the Statement Is True or False? Justify Your $x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0$

Determine whether the statement is true or false? Justify your answer. ​
The graph of the equation $x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0$ where, $k$ is any constant less than $\frac { 1 } { 4 }$ ,is a hyperbola.
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A) False.For the graph to be a hyperbola,the discriminant must be less than zero.
B) True.For the graph to be a hyperbola,the discriminant must be greater than zero.

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