Learn how to graph a hyperbola

Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola.

Next, we identify the characteristics of the given hyperbola. The center of the hyperbola is (h, k). It is halfway between the two vertices and halfway between the two foci. 'a' (the distance from the center to the vertices) is the square root of the first denominator and 'b' (the` distance from the center to the covertices) is the square root of the second denominator. 'c' (the distance from the center to the foci) is obtained by taking the square root of the sum of a^2 and b^2. Using these characteristics of the hyperbola, we can graph the asymptotes of the hyperbola and hence graph the hyperbola.

Note that a hyperbola is vertical when it is facing up and down and is horizontal when it is facing right and left.
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections

[LukeK]

Brian, you're a great teacher (and a life saver)

[sararobertson]

Your videos may be the only reason I pass college level algebra. Thank you!

[justinjustin]

6:38 for those who dont get why k was equal to 3, you’re welcome :))

[bananabeast]

Watching you teach makes me realize how much my teacher sucks

[honruvian]

Since the formula for asymptotes goes h, k wouldn't k be -2 because it is horizontal? Formula for vertical is k, h right?

[kingvirginiaverg]

Best math teacher. Have to come for you for my finals since I completely forgot about this. Thank you very much for such great content.

[lynnsanchez]

You are a great teacher, i get to know the equations when you were the one who explains how, my teacher, I really didn't get every single thing from her, thanks Sir Brian!!!!


High School Student here!!!

[gabbyphan]

My teacher suggests to draw a rectangle between the two vertices using a and b so that the asymtotes of the hyperbola go through the corners of the rectangle

[SW-nxjz]

Very helpful video! Thanks so much for uploading such great content. I can actually understand

[RogersJimmy-nq]

What I've learned from you're videos is that even teachers and great mathematicians make mistakes.

[chelseasharleneamoslo]

Sir your another y should be -2x +3 since we minus positive 5 to - 2, but the rest is brilliant, I easily get it. Thanks to you

[odie-wankenodie]

Thankyou! My professor is putting this on the test even though he never got to this section....

[the_unknownbattlefront]

Uhm sir, its a very good video you have :). It can easily be understood compared to the actual lessons I take at school lol I give you a thumbs up but the center is represented as (h, k). Why is the 'k' on getting the asymptote is '3'? Then on 'h' is '-2'? Wasn't the center (3, -2)?


Edit: Whoops I should've watched the whole video 😂😆 sorry about that sir hahaha thanks for the vid! it truly helps.

[randomthoughts]

It's good to have you as our life savwry

[koysensei]

@ 8:23, how do i know the values of the pattern, "up two, over one" where did that pattern come from? Thanks!

[bossgamer]

Hey, just wanted to start with great video! I really do enjoy your content. I was wondering if I subscribed would i get notified when you upload a new video? I would really love that instead of always coming back to your channel. Thanks!

[jennyguzman]

Isn't the a² is dominant so 16 should be a² because it is much bigger than 4?

[hfsubliminal]

Wait I’m kinda confused cause isn’t ur b^2 bigger than ur a^2 cause it’s 16? so wouldn’t it be vertical instead of horizontal?

[romyow]

Hello where did the 2 vertex get from?

[bradpotts]

i cant find any videos explaining what to do if the equation doesn't equal to 1