$\"\"$

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Foci of the ellipse $\"\"$ and vertices are $\"\"$ .

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The $\"\"$ coordinate in foci and vertices are same, so the ellipse is vertical.

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Standard form of horizontal ellipse $\"\"$ , where $\"image\"$ .

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$\"image\"$ is length of semi major axis and $\"image\"$ is length of semi minor axis.

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Center is $\"\"$ , vertices $\"\"$

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Foci $\"\"$ and $\"image\"$ .

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$\"\"$

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Vertices are $\"\"$ .

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The $\"\"$ coordinate of center is 0.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Center is $\"image\"$ .

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$\"\"$

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Find the values of $\"image\"$ , $\"image\"$ .

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Substitute $\"\"$ in equation (1).

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$\"\"$

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$\"\"$

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Foci $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in equation (3).

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$\"\"$

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$\"\"$ .

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$\"image\"$ is the distance from center to each focus.

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$\"\"$

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$\"\"$

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Substitute $\"image\"$ , $\"\"$ and $\"\"$ in standard form.

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$\"\"$

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$\"\"$

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The ellipse equation is $\"\"$ .