Question 1150067
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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<br>
{{{x^2/76^2-y^2/b^2 = 1}}}<br>
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).<br>
Use those coordinates in the equation to determine b^2.<br>
{{{136^2/76^2-(-366)^2/b^2 = 1}}}
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Solve for b^2 using basic algebra....<br>