Answer:
C. Hyperbola opening up and down
Explanation:
A graph tells the tale.
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The term with the positive coefficient identifies the axis along which the hyperbola opens. Here, that is the y-axis, so the figure opens up and down.
The minus sign between the squared terms indicates it is a hyperbola, rather than a closed curve (ellipse or circle). The fact that both terms are squared indicates it is not a parabola.