Answer
The equation of the circular is
${{x}^{2}}+{{\left( y-82 \right)}^{2}}=4624$.
Work Step by Step
The center of the rectangular system is on the ground directly below the wheel.
The wheel has the radius of 68 feet and the clearance between the wheel and the ground is 14 feet. So, the perpendicular distance between the origin to the center of the wheel is 82 feet.
Suppose that the line perpendicular to the ground is $y\text{-axis}$; the coordinates of the center of the wheel are $\left( 0,\ 82 \right)$.
Let any point $\left( x,\ y \right)$ be on the wheel. Since the radius is 68 feet, the distance between any point on the wheel and its center will be equal to 68.
Now apply the distance formula and use the values.
$d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}$
Suppose ${{x}_{2}}=x\ \text{ and }\ {{x}_{1}}=0,\ {{y}_{2}}=y\,\,\text{ and }\,\,{{y}_{1}}=82$ and use the values in the distance formula as
$\begin{align}
& 68=\sqrt{{{\left( x-0 \right)}^{2}}+{{\left( y-82 \right)}^{2}}} \\
& {{68}^{2}}={{\left( x-0 \right)}^{2}}+{{\left( y-82 \right)}^{2}} \\
& 4624={{x}^{2}}+{{\left( y-82 \right)}^{2}}
\end{align}$
or ${{x}^{2}}+{{\left( y-82 \right)}^{2}}=4624$
