$\"\"$

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From the figure :

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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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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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From the figure $\"\"$ and $\"\"$ .

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Major axis of the ellipse is $\"\"$ .

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Minor axis of the ellicpse is $\"\"$ .

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Equation of the ellicpse can be obtained by substiuting $\"\"$ and $\"\"$ in the equation of the ellicpse $\"\"$ .

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$\"\"$

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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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Therefore foci is at $\"\"$ .

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$\"\"$

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The equation of the ellicpse is $\"\"$ and has foci at $\"\"$ .