Ses
a 14 foot ladder is leaning against a building. the ladder makes a 45 degree
angle with the building. how far up the building does the ladder reach?

what is the answer to this

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.

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.