$\"\"$

\

(a)

\

The narrowest width of a hyperbola with a horizontal orientation corresponds to the length of the transverse axis.

\

Standard from of the horizontal hyperbola is $\"\"$ .

\

Find $\"\"$ values.

\

In this case, $\"\"$

\

$\"\"$

\

$\"\"$ .

\

The tower eccentricity is $\"\"$ .

\

Eccentricity $\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute the values $\"\"$ and $\"\"$ in standard form.

\

$\"\"$ .

\

$\"\"$

\

(b)

\

If the top of the tower is 32 meters above the center of the hyperbola and the se is 76 meters below the center.

\

Graph the hyperbola and the the horizontal lines $\"\"$ and $\"\"$ in same screen.

\

Identify the intersecting points.

\

$\"\"$

\

Observe the graph:

\

The line $\"\"$ is intersecting the hyperbola at $\"\"$ and $\"\"$ .

\

Therefore, radius of the top of the tower is $\"\"$ .

\

The line $\"\"$ is intersecting the hyperbola at $\"\"$ and $\"\"$ .

\

Therefore, radius of the base of the tower is $\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) Radius of the top of the tower is $\"\"$ .

\

Radius of the base of the tower is $\"\"$ .