What is the difference between finding the area as a PRODUCT and finding the area as a SUM? Do you end up with the same answer
for both? Why is that?

hi! i think the answer is 1/2 : )

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.

130 degrees. i have no other way to explain