Equation of ellipse $\"\"$ .

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The general equation of ellipse through the center $\"\"$ is

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$\"\"$

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In the given equation $\"\"$ , $\"\"$ .

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

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Every ellipse has symmetry with respect to two axis, one is major axis and another one is minor axis.

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Length of major axis is 2b and length of minor axis is 2a.

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\ \ The end points of these two axes can be determined as

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End points on major axis $\"\"$

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$\"\"$

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$\"\"$

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End points on minor axis $\"\"$

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$\"\"$

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$\"\"$

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Now plot these points on the graph and draw the ellipse.

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$\"\"$

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In this way you can find the graphs of other ellipses.

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Now you can also find the equation of an ellipse with its graph by finding its center,

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length of major and minor axis.

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Let us take the graph of above given equation

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$\"\"$

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From the graph

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

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The length of major axis is $\"\"$ , therefore $\"\"$ .

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The length of minor axis is $\"\"$ , therefore $\"\"$ .

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So, the equation of the ellipse is $\"\"$ .