$\"\"$

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(a)

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Eccentricity of the racetrack is $\"\"$ .

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Length of the elliptical track is $\"\"$ ft.

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Elliptical track is in the form of horizontal ellipse.

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Therefore,

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$\"\"$

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The standard form of horizontal ellipse $\"\"$ .

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Eccentricity : $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Therefore, maximum width of the track is $\"\"$ feet.

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$\"\"$

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(b)

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Find the equation for the ellipse If the origin is located at the center of the race track.

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The ellipse equation with center at the origin is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$ .

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$\"\"$

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(a) The maximum width of the track is $\"\"$ feet.

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(b) $\"\"$ .