#### Answer

Hyperbola shifted 3 units down and 1 unit right

#### Work Step by Step

This conic is a hyperbola. Notice from the graph that the center of the hyperbola is shifted 1 unit right and 3 units down. This can be verified from the equation:
$\frac{(y+3)^2}{4}-(x-1)^2=1$
The $(y+3)$ means that the center is shifted three units down (down the y-axis). The $(x-1)$ means that the center is shifted right one unit (across the x-axis).