$\"\"$

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The standard form of vertical ellipse is $\"\"$ .

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Where

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$\"\"$ ,

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$\"\"$ ,

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$\"\"$ : length of semi major axis,

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$\"\"$ : length of semi minor axis,

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Center : $\"\"$ ,

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Foci : $\"\"$ ,

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Vertices : $\"\"$ ,

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Co-vertices : $\"\"$ ,

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Major axis : $\"\"$ ,

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Minor axis : $\"\"$ .

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$\"\"$

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The ellipse equation is $\"\"$ .

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Convert the equation into standard form of ellipse by using completing square method.

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$\"\"$

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$\"\"$

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To change the expressions $\"\"$ and $\"\"$ into a perfect square trinomial, $\"\"$ and $\"\"$ to each side of the equation.

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$\"\"$

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$\"\"$ .

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$\"\"$

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The ellipse equation is $\"\"$ .

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Compare the equation with $\"\"$ .

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

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$\"\"$ .

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Use these values to determine the characteristics of the ellipse.

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Since $\"\"$ , it is a vertical ellipse.

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Center : $\"\"$ .

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Foci : $\"\"$ .

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Vertices : $\"\"$ .

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Co-vertices : $\"\"$ .

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Major axis : $\"\"$ .

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Minor axis : $\"\"$ .

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$\"\"$

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Graph the center, vertices, foci, and axes.

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Make a table of values to sketch the ellipse.

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The ellipse equation is $\"\"$ .

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Solve for $\"\"$ .

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$\"\"$

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$\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\"\"

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$\"\"$

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\"\"

\"\"

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$\"\"$

\

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$\"\"$

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$\"\"$

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\"\"

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$\"\"$

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$\"\"$

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$\"\"$

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Plot the points and sketch the ellipse.

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Graph :

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Graph of $\"\"$ :

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$\"\"$ .

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$\"\"$

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Graph of $\"\"$ :

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$\"\"$ .