The Graph of the Equation $x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0$

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.