Question 971199
The cross section of a 12 - foot -high cooling tower is in the form of a hyperbola. its top and bottom parts are 8 feet wide and the narrowest part is 4 feet. A man painting the tower must place a horizontal plank exactly spanning the upper 6 feet width of the cross section of the tower. At what point from the ground should the plank be placed? 
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The cooling tower can be represented by a hyperbola with horizontal transverse axis with center at the origin.
Its standard form of equation: {{{x^2/a^2-y^2/b^2=1}}}
For given problem:
a=2 (distance from center to vertices(the narrowest part)
a^2=4
solve for b^2 using coordinates (4, 6) of the point at the top right corner of the tower
{{{x^2/a^2-y^2/b^2=1}}}
{{{4^2/4-6^2/b^2=1}}}
{{{16/4-36/b^2=1}}}
36/b^2=4-1=3
b^2=12
equation: {{{x^2/4-y^2/12=1}}}
plug in coordinates(3, y) of the point at the top right corner of the horizontal plank and solve for y
{{{x^2/4-y^2/12=1}}}
{{{3^2/4-y^2/12=1}}}
9/4-1=y^2/12
5/4=y^2/12
y^2=15
y=√15=3.87
At what point from the ground should the plank be placed? 3.87 ft