# Slant Asymptote Lines: Example 2: Horizontal Hyperbola

2

• 19
• 0
• 0.496

• Published on Nov 15, 2020

In this video I go over another example on Slant Asymptotes and this time look at the slant asymptote lines of a horizontal hyperbola, which is a hyperbola that extends outwards horizontally. The hyperbola x2/a2 – y2/b2 = 1 where a and b are constants has slant asymptote lines y = +/- (b/a)x. This is proven by applying the definition of slant asymptotes which I covered in my earlier video, and that is the limit as x approaches infinity of the difference between the function and a line approaches zero. In other words the function, in this case the hyperbola, approaches the asymptote lines. In proving this, I first rearrange the hyperbola to write it as y = f(x). But since the function involves square rooting a square, we get a two part function that can be either positive or negative, and thus to save time I combined all of the +/- terms (as well as the limit as x approaches +/- infinity) in just one limit formula. This was a shortcut on my part, but nonetheless the result is the same for this particular example as compared with doing it individually. I will be referencing this example on slant asymptotes for a horizontal hyperbola in my later videos, so make sure you watch this video and understand the derivation!

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/slant-asymptote-lines-example-2-horizontal-hyperbola

Related Videos:

Slant Asymptote Lines: Example 1: Rational Function: https://youtu.be/FT5yNtPeBvg
Slant Asymptote Lines + Special Case: Rational Functions and Long Division: https://youtu.be/QX2nfi5JtQs
Hyperbola - Definition and derivation of the equation: x2/a2 - y2/b2 = 1: http://youtu.be/Y6iYC4VEAi0
Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI .

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: contact@mes.fm

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

###### Tags :

To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

02:20
7 views a year ago \$
20:59
8 views 3 months ago \$
18:45
5 views 4 years ago \$
16:29
16 views 11 months ago \$
10:38

#### More Videos

19:25
2 views a year ago \$
17:46
09:29
1 views 7 months ago \$
01:55
7 views 3 months ago \$
31:44
40:56
6 views 3 years ago \$
03:44
32 views 2 years ago \$
06:29
1 views 2 months ago \$
01:25:45
10 views 3 years ago \$
09:22
00:16
1 views 2 years ago \$
50:30
18 views 3 years ago \$
17:29
1 views 3 years ago \$
12:58
5 views 4 months ago \$
57:28
05:09
22 views a year ago \$
01:34
1 views 16 hours ago \$
03:44
31 views 3 years ago \$
01:20
1 views 7 months ago \$
02:25
07:42
39 views 3 years ago \$
25:39
17 views 3 years ago \$
26:08
75 views 3 years ago \$
05:05
4 views 3 years ago \$
09:33