$\"\"$

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(a)

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The shape of a roller coaster loop in an amusement park is $\"\"$ .

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The value of $\"\"$ is always greter than the The value of $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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$\"\"$

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Find the width of the loop along the horizontal line $\"\"$ .

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$\"\"$ .

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The width of the loop along the horizontal line is $\"\"$ .

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$\"\"$

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(b)

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The lower rail is $\"\"$ from ground level.

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The maximum height of the roller is $\"\"$ .

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Find the value of $\"\"$ .

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$\"\"$

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Thus, the maximum height of the roller is $\"\"$ .

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$\"\"$

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(c)

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Eccentricity of the ellipse : $\"\"$ .

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Find the value of $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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(a) The width of the loop along the horizontal line is $\"\"$ .

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(b) The maximum height of the roller is $\"\"$ .

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(c) Eccentricity of the ellipse is $\"\"$ .