The arch is in the shape of semi ellipse.

The major axis length is .

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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 .

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The equation of the ellipse is .

The road way is above the axis of the ellipse.

At the center, the road way is above the arch.

At a point  either side of the center, .

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The vertical distance from the road way to arch is .

At a point  either side of the center, .

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The vertical distance from the road way to arch is .

At a point  either side of the center, .

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The vertical distance from the road way to arch is .

The equation of the ellipse is .

The vertical distance from the road way to arch in respective interval of five units are , and .