In this video I go over another example on Slant Asymptotes and this time determine the slant asymptote lines of a vertical hyperbola. Recall from my last video in which I determined the slant asymptote lines of a horizontal hyperbola of the formula x^2/a^2 – y^2/b^2 = 1. Now the difference between a horizontal and a vertical hyperbola is that we switch the x and y variables to instead come up with the formula: y^2/a^2 – x^2/b^2 = 1. In the horizontal hyperbola example, I showed that the slant asymptote lines were y = +/- (b/a)x. And in this video I show that for a vertical hyperbola, all we have to do is just switch the a and b constants in the asymptote lines equation to get instead: y = +/- (a/b)x. The proof that these are in fact slant asymptote lines to the vertical hyperbola is almost identical to the derivation for the horizontal hyperbola. This should be the case because essentially horizontal and vertical hyperbolas are the exact the same but rotated by 90 degrees, thus opening up on either the x-axis (horizontal hyperbola) or y-axis (vertical hyperbola). This is a very good example in understanding the differences and similarities of vertical and horizontal hyperbolas so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5FDqbSRsWVoj9-Xmg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/slant-asymptote-lines-example-3-vertical-hyperbola
Related Videos:
Slant Asymptote Lines: Example 2: Horizontal Hyperbola:
Slant Asymptote Lines: Example 1: Rational Function:
Slant Asymptote Lines + Special Case: Rational Functions and Long Division:
Hyperbola - Definition and derivation of the equation: x^2/a^2 - y^2/b^2 = 1:
Limits at Infinity: Horizontal Asymptotes: .
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I love the way you can explain Math.
Are you interested about making videos and articles about sciences such as Cybernetics and Occults knowledge such as the Kabbalah here on MES?
Thanks for asking! I've looked up Cybernetics this past month was very interested in it. The Kabbalah is something I need to look at too. Maybe in the near future I can get down to investigating them further and make videos. But main point of my channel is to present a blue-print for others on both learning and teaching. So maybe if you are interested covering such topics in a MES-like fashion, I can upload your work here and give it the MES Seal of Approval!
The kabbalah offer very great fundations to all occult and esoteric knowledge practiced by a few, I would be interested in publishing article about it here on MES if it gets the "MES Seal of Approval" ^^
Here is a very interesting approach by taking the wonderful lens of cybernetic/scientific to study of unreal/esoteric knowledge/process which I would try to get as close as in term of quality.