Shifted Conics: Example 3: Ellipse

in #mathematics6 years ago (edited)

In this video I go over another example on shifting conics and this time shift a horizontal ellipse while being given just the coordinates of the foci and vertices. Since the foci and vertices all have the same y-coordinate, they are thus located on the same horizontal line, y = -2, and thus the ellipse is stretched horizontally. Using the coordinates of the foci and vertices, we can determine the center of the ellipse and the c, a, & b values. Thus we can just input these values into a generic ellipse but shift it to the new center in the same methodology shown in my earlier video. This is a very detailed video into determining the parameters of an ellipse from the coordinates of its foci & vertices, and then shifting it, so make sure to watch this video!


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Shifted Conics Example 3 Ellipse.jpeg

Example:

Find an equation of the ellipse with foci (2, -2), (4, -2) and vertices (1, -2), (5, -2).

https://www.desmos.com/calculator/2btb2iarx4
Retrieved: 1 February 2018
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