$\"\"$

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The vertices of the ellipse equation are $\"\"$ , $\"\"$ ;

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The foci of the ellipse equation are $\"\"$ , $\"\"$ ;

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Here the $\"\"$ co-ordinate are equal, hence major axis is along $\"\"$ -axis.

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Hence the vertices and foci are $\"\"$ and $\"\"$ .

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The center is the mid point point of focus of the hyperbola.

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Center $\"\"$ .

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The distance between center and vertex is $\"\"$ .

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The distance between center and focus is $\"\"$ .

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Therefore, $\"\"$ , $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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For an ellipse : $\"\"$ .

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$\"\"$

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From problem (41) :

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The parametric equations for ellipse equation are $\"\"$ and $\"\"$ .

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

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$\"\"$

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

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$\"\"$

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The parametric equations for ellipse equation are $\"\"$ and $\"\"$ .

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$\"\"$

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The parametric equations for ellipse equation are $\"\"$ and $\"\"$ .