a) Assuming that radio signals travel at a speed of 980 ft/µs, find an equation of the hyperbola on which the ship lies.
focs (-200,0) (200,0) c=200.
⎮⎮AP⎮-⎮BP⎮ =1200x980=1176000ft =2450/11mi
⎮⎮AP⎮-⎮BP⎮=2a
2a=2450/11mi , a=1225/11mi
b^2=c^2-a^2, 40000-(1225/11)^2 =27598.1405
b) If the ship is due north of B, how far of the coastline is the ship?
x=200 y=?
x^2/12401.8595 - y^2/27598.1405=1
200^2/12401.8595 - y^2/27598.1405=1
-y^2/27598.1405=1-40000/12401.8595
y^2=(-61414.77083)/-1 y=247.8 =248
focs (-200,0) (200,0) c=200.
⎮⎮AP⎮-⎮BP⎮ =1200x980=1176000ft =2450/11mi
⎮⎮AP⎮-⎮BP⎮=2a
2a=2450/11mi , a=1225/11mi
b^2=c^2-a^2, 40000-(1225/11)^2 =27598.1405
b) If the ship is due north of B, how far of the coastline is the ship?
x=200 y=?
x^2/12401.8595 - y^2/27598.1405=1
200^2/12401.8595 - y^2/27598.1405=1
-y^2/27598.1405=1-40000/12401.8595
y^2=(-61414.77083)/-1 y=247.8 =248