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Conic Sections: Ellipses: Example 2: Vertical Ellipse

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First published at 02:04 UTC on November 20th, 2017.

Math Easy Solutions

MES

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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!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvlL0Dro9YGOWlSH2g

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-conic-sections-ellipses-example-2-vertical-ellipse

Related Videos:

Conic Sections: Ellipses: Example 1: https://youtu.be/m9FXGv3kMkk
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Ellipses: Definition and Proof of Equation: http://youtu.be/tvfNgT4CrFs
Inverted Ellipses: http://youtu.be/NQQFj66-bxA
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I .

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