Step 1:

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The ellipse equation is $\"\"$ .

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Write the equation in standard form of ellipse.

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$\"\"$

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Complete the each square.

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$\"\"$

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Compare it to standard form of the ellipse equation is $\"\"$ .

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Here $\"\"$ , so major axis is parallel to $\"\"$ axis.

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Where,

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$\"\"$ is the center of the ellipse.

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$\"\"$ is the length of the semi major axis.

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$\"\"$ is the length of the semi minor axis.

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$ .

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Step 2:

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The center of the ellipse is $\"\"$ .

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The vertices of the ellipse are $\"\"$ .

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The foci of the ellipse are $\"\"$ .

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The end points of the minor axis is $\"\"$ .

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Graph :

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(1) Draw the coordinate plane.

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(2) Plot the center, foci and vertices.

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(3) Draw the equation of the ellipse.

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$\"\"$

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Solution :

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The center of the ellipse is $\"\"$ .

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The vertices of the ellipse are $\"\"$ .

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The foci of the ellipse are $\"\"$ .

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Graph of the ellipse :

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$\"\"$