Question

(((y+3)^2)/9)-(((x-2)^2)/16)=1
Write the equations of the two asymptotes.

Answer 1

That's a hyperbola with center at (2,-3), right?

Answer 2

That's what it looks like to me.
Can you see the asymptotes in the diagram? You can write equations for the lines from their slopes and the point they both pass through (the center)