$\"\"$

The arch is in the shape of semi ellipse.

Observe the diagram:

The major axis length is $\"\"$ .

$\"\"$ .

The length of semi minor axis is $\"\"$ .

The major axis of ellipse along the $\"\"$ -axis.

Consider the center at origin.

The standard form of horizontal ellipse center is at origin is $\"\"$ .

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

The equation of the ellipse is $\"\"$ .

$\"\"$

The equation of the ellipse is $\"\"$ .