Bart and sam played a game in which each player earns or loses points in each turn. a player's total score after two turns is the sum of his points earned or lost. the player with the greater score after two turns wins. bart earned 123 points and lost 180 points. sam earned 185 points and lost 255 points. which person won the game? explain.

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.