SOLUTION: I have a problem "The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tower is 272 feet. The smallest diameter of the tower is 152
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Question 1150067: I have a problem "The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tower is 272 feet. The smallest diameter of the tower is 152 which is 366 feet above the ground. The tower is 522 feet tall."
What is the width of the tower at a height of 56 feet? Answer by greenestamps(13200) (Show Source):
Let the origin of a coordinate system be at the center of the tower at the height where the diameter is minimum. Since that minimum diameter is 152, one of the vertices of the hyperbola is at (76,0). The equation in standard form is then
The other known point on the hyperbola is the base of the tower. Since the center of the hyperbola is 366 feet above the base of the tower, and since the diameter of the base of the tower is 272 feet, the coordinates of that point are (136, -366).
Use those coordinates in the equation to determine b^2.
