Slant Asymptote Lines: Example 3: Vertical Hyperbola

over 3 years ago (Edited)

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 x²/a² – y²/b² = 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: y²/a² – x²/b² = 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 the Hive blockchain: https://peakd.com/mathematics/@mes/slant-asymptote-lines-example-3-vertical-hyperbola