Inverted Ellipses

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In this video I go over inverted ellipses which are basically vertical ellipses or have the foci on the y axis. The inverse of the ellipse is found by simply switching the x and y variables.


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Inverted Ellipses

Inverted Ellipses.jpeg

Recall from my previous video on ellipses:

The equation of an ellipse is:

And has foci (+/- c, 0), where c2 = a2 - b2, and vertices (+/- a, 0).

If the foci of an ellipse are located on the y-axis (0, +/- c), then we can find its equation by interchanging x and y:

Thus the equation of an inverse ellipse is:

And has foci (0, +/-c), where c2 = a2 - b2, and vertices (0, +/- a).



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