Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 16 meters wide. The center of the arch is 6 meters above the center of the river (see the figure). Write an equation for the ellipse in which the $x$-axis coincides with the water level and the $y$-axis passes through the center of the arch.

Step 1 ：The equation of an ellipse centered at the origin with semi-major axis a and semi-minor axis b is given by: \((x/a)^2 + (y/b)^2 = 1\)

Step 2 ：In this case, the semi-major axis a is half the width of the river, which is 16/2 = 8 meters. The semi-minor axis b is the height of the arch above the river, which is 6 meters.

Step 3 ：So the equation of the ellipse is: \((x/8)^2 + (y/6)^2 = 1\)

Step 4 ：Final Answer: The equation of the ellipse is \(\boxed{\frac{x^2}{64} + \frac{y^2}{36} = 1}\)