Conic Sections: Ellipses: Example 2: Vertical Ellipse

In this video I go over another example on conic sections and ellipses, and this time look at determining the equation of an ellipse when we are given the foci (plural for focus) and the vertices. In this particular example, since the foci (0 , +/- 2) and vertices (0 , +/- 3) are on the y-axis, we obtain a vertical ellipse. Thus we use the formula for an ellipse that involves the a^2 term below the y^2 term: x^2/b^2 + y^2/a^2 = 1. Then all we need to use the definition of b^2 = a^2 – c^2 from my derivation video for ellipses, to get b^2 = 5. Note that b corresponds to the end points on the minor axis of the ellipses, whereas the vertices correspond to the end points on the major axis. From here we get the ellipse x^2/5 + y^2/9 = 1 or 9x^2 + 5y^2 = 45. This is a simple but very detailed look at determining the equation of a vertical or inverted ellipse so make sure to watch this video!

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[mes]

I don't always derive the equation of an ellipse but when I do I'm usually given the foci and vertices, and it's usually vertical ;)