Question 691504
the cross section of a nuclear power plant cooling tower is in the shape of a hyperbola. suppose the tower has a base diameter of 228 meters and the narrowest point, 72 meters above ground is 76 meters. if the diameter at the top is 152 meters. how tall is the tower
***
Draw a sketch of a hyperbola with a base=228.
Length of horizontal transverse axis=76
Top=152
Set center at origin (0,0)
right endpoint of base: (114,-72)
Equation of hyperbola:x^2/a^2-y^2/b^2=1
given length of horizontal transverse axis=76=2a
a=38
a^2=1444
Using coordinates from endpoint of base, solve for b^2
Equation: 114^2/1444-72^2/b^2=1
114^2/1444-72^2/b^2=1
9-5184/b^2=1
5184/b^2=8
b^2=5184/8
b^2=648
Equation: x^2/1444-y^2/648=1
plug-in x=76, then solve for y
76^2/1444-y^2/648=1
4-y^2/648=1
y^2/648=3
y^2=3*648=1944
y≈√1944≈44.1
height of tower≈y+72≈116.1 meters