Ex 1: Graph an Ellipse with Center NOT at the Origin and Horizontal Major Axis

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This video provides an example of how to graph the standard equation of an ellipse with the center not at the origin and a horizontal major axis.
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Thanks a lot ! I wanna ask if the ellipse isn't centered at origin like the one in the video, does that affect our work with integrals to deduce the surface or no ?
I am having trouble working with integrals if the ellipse isn't centered at origin. Please help!

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how da hell you get foci= (-3, -√7, 2)&(-3, √7, 2) ?

caguranganjohnrussels.