Step 1:

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

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

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

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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 $\"image\"$

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

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Step 2:

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Vertices $\"\"$

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The $\"image\"$ 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 $\"image\"$ .

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Step 3:

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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 $\"image\"$ .

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$\"\"$

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$\"\"$

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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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$\"\"$

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$\"image\"$

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Step 4:

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

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$\"image\"$

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$\"image\"$ .

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Solution:

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The ellipse equation is $\"image\"$ .