ANSWER
Hyperbole.
EXPLANATION
The given equation is
[tex] - {x}^{2} + 4 {y}^{2} - 6x - 48y + 139 = 0[/tex]
We use the sign of the quadratic terms to determine whether the conic is a hyperbole or an ellipse.
Since the sign of the coefficient of the quadratic terms are opposite, the conic is a hyperbole.
