Conic Sections: Ellipses: Example 1

In this video I go further into conic sections and this time go over an example on graphing the ellipse 9x² + 16y² = 144, as well as locate its foci (plural for focus). Since this equation is not written in the standard form for an ellipse, x²/a² + y²/b² = 1, we need to do some algebra to make it into that form. We can do this by dividing both sides by 144 to get the right side equaling 1, and the left side obtaining the a and b values. The a value corresponds to the vertices of the ellipse, which in this case are the x-intercepts because that is where the major axis lies under. The b-value corresponds to the y-intercepts. To obtain the foci we can use the definition from my last video, c² = a² – b², from which we can solve the c-value which corresponds to the foci. Putting this all together we can than sketch the ellipse, which is a horizontally flat ellipse. This is a very detailed look at going about sketching a specific ellipse, so make sure to watch this video!

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Related Videos:

Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles):

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