$\"\"$

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The ellipse is $\"\"$ .

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$\"\"$

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Divide each side by $\"\"$ .

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$\"\"$

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The ellipse is centered at $\"\"$ .

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Since it is centered at $\"\"$ the standard form of the equation of the ellicpse is

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$\"\"$ .

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Where $\"\"$ and $\"\"$ .

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If $\"\"$ then $\"\"$ and $\"\"$ are lengths of major and minor axis.

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If $\"\"$ then $\"\"$ and $\"\"$ are lengths of major and minor axis.

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$\"\"$

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The equation of the ellicpse is $\"\"$ .

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The ellipse which is in the form of $\"\"$ ,

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if $\"\"$ , then the foci is $\"\"$ where $\"\"$ .

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if $\"\"$ , then the foci is $\"\"$ where $\"\"$ .

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$\"\"$ .

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Where $\"\"$ and $\"\"$ .

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$\"\"$

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Therefore $\"\"$ .

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Therefore foci is at $\"\"$ .

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Vertices is at $\"\"$ .

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$\"\"$

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Graph :

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(1).Draw the coordinate plane.

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(2).Graph the ellipse $\"\"$ .

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$\"\"$

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Observe the graph:

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The Blue colour represents the foci $\"\"$ .

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The Green colour represents the vertices $\"\"$ .

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$\"\"$

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Graph the ellipse $\"\"$ :

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$\"\"$