at a real estate agency, an agent sold a house for $327,000. the commission rate is 5.5% for the real estate agency and the commission rate for the agent is 30% of the amount the real estate agency gets. how much did the agency make on the house? how much did the agent earn in commission?

you can use a^2+ b^2=c^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.