ANSWER
Hyperbola
EXPLANATION
The given conic has equation:
[tex] {x}^{2} - {y}^{2} = 16[/tex]
We divide through by 16.
[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = \frac{16}{16} [/tex]
We simplify the right hand side to get
[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = 1[/tex]
Or
[tex] \frac{ {x}^{2} }{ {4}^{2} } - \frac{ {y}^{2} }{ {4}^{2} } = 1[/tex]
This is a hyperbola, that has its vertex at the origin because the quadratic terms have different signs. One is positive and the other is negative.
