Finding the vertices, foci and asymptotes of 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

[@elisabethmaldonado9111]

B/A would be 1/2 not 1/4

[@brianmclogan]

yes Elisabeth! great catch! I have pinned your comment so others are not confused

[@katiem8025]

He fixed it in the video

[@pat1373]

@Chris Abram 🧢, it's probably a sight where you gotta pay or download xyz games

[@franman6076]

3:21 he gave that man who started singing the death stare lmaooo

[@scottyscott7587]

3:23 lmao at whoever sang the "c"

[@dj2kbased]

LMAOOOO 😂😂😂😂

[@powell3463]

He sang a 'G' actually

[@benbillings3237]

Jay Wu ah but fuck u tho

[@benbillings3237]

Jay Wu just watch the math

[@scarlethart7857]

I don't think you know what that means...

[@jdmender3128]

Been studying for hours and reading my notes couldn't understand it…. Watched a few 8 min videos and learned so much, Thank you

[@brianmclogan]

Jd Mender you are very welcome! happy to be able to help you out!

[@syandaemanuel1342]

Jd Mender same to me,its woow

[@DevastatorXD03]

3:23 Very off topic but that dude who said that long "C" And that moment of silence for 3 seconds made me laugh 😂 But thanks for this video! I was so stuck on finding vertices and foci for hyperbola's, you helped a lot!

[@ThatweirdEMTnerd]

Me too! I was looking for someone to talk about it 😂

[@BuZGaming]

If every teacher was as clear as you are, then people could stress less about school. Thanks once again for an amazing lesson Mr. Mclogan! :D

[@brianmclogan]

you are very welcome! happy to be able to help you out!

[@gavinmatsu]

I just had spring break and forgot how to do my homework. The first 3 minutes of this helped me remember exactly how to do it

[@nanasparkl3]

I've been watching your videos for a year now and they've always helped, thank you so much for explaining everything so well!!

[@brianmclogan]

you are very welcome! happy to be able to help!

[@doomslayer3294]

....dude, my teacher explained this on 2 different classes, and i could understand this at all. saw this video, and am now doing all of my exercises right. great teacher!

[@zachstarattack7320]

God's gift to man! Studying before my final and this refresher was just what the doctor ordered!

[@brianmclogan]

Perfect!!

[@strongandhealthy1111]

Thank You!! This makes complete sense FINALLY!

[@ayanbehjat4265]

at 3:23 best part

[@brianmclogan]

Ayan Behjat haha funny

[@SinjidKhan]

+Ayan Behjat Then Mr. McLogan's reaction, haha.

[@indefinite115]

Thanks for uploading these man My teacher doesn't really teach, so I basically rely on these videos along with a mélange of other videos

[@SinjidKhan]

Damn bro, you just brought me to the past. It's been almost a year.

[@indefinite115]

Time flies, especially as you grow older. One year is 1/5 of your life when you're five years old, but one year is just 1/16 of your life at the age of 16. This causes years to go by quicker and quicker as your grow older. I felt like you might be thinking about that stuff rn

[@justinsin9423]

thank you birria brian you carry me so much during precalc you will always have my blessing

[@mikyllaguigayoma8241]

I know I can always rely on your videos, sir!! Thank you very much 💖💖

[@brianmclogan]

You are very welcome!!

[@sue-sageasmr2020]

Great explanation! Thank you!

[@JeeterMCHeater]

Getting me through pre-cal man, you're a life saver

[@kwame1015]

3:22 XDD He was about to smack the shit outta him.

[@brianmclogan]

no, would never do that

[@raultorres847]

hahaha I saw it and I went right to the comments

[@westsidenikkaboi4090]

Brian McLogan he was joking

[@iceicebaby_09]

Your video made me pass my precal! Thank you for this!!:)

[@somethingsomewhere509]

will have midterm exams in pre-calc next week. thank you for this. wish me luck!

[@amanlrwtfsm1323]

Thanks,,cuz I was very much confused in this particular eqn. 👌🏻

[@FaroukHussienSaripBSarip]

Thank you sir, you are one of the reason why i survive my math subjects, your making it easy for me💓

[@al-jamebalina5339]

Thank you sir, this helped me a lot.

[@GeoCalifornian]

Brian McLogan your straightforward explanations are terrific. Brian McLogan is the McMan. /Regards

[@LedCODprductions]

I am an online student and watch your videos everyday now. You teach the material so thoroughly that I haven't had a question yet. Thank you!

[@brianmclogan]

+Hunter Mill that is great to hear Hunter, pleased to be able to assist you this year

[@fishsticks3729]

But for a vertical hyperbola, do I still do c^2=a^2+b^2 I’m so confused when it comes to verticals because everyone says smthn different

[@jeffreyhernandez9682]

You sir, are a blessing

[@brianmclogan]

you better! good luck and let me know how you do

[@slashmaster7690]

You are a legend. Was stuck on an asymptote forever and this got it in like 2 seconds!

[@tashasolorzano8545]

omg genius man!!!! ty sooo much i have a quiz tomorrow!!!! hope i remebemer!!!

[@ezrayitbarek2875]

Year 2021 and the math never changes .... thanks teacher

[@paulsigalat9646]

I actually try it first and recorrecting by watching your equation and guest what... we've matched up. Thanks

[@urmisoneji5719]

Thank you! This was Really helpful!

[@brianmclogan]

+Urmi Patel sweet, glad I could help you!

[@muzamilmahtab5588]

Great teacher... ❤

[@azuurasmr7937]

All this coughing gonna get me infected thru my phone in 2020

[@KeziahAyala]

how to solve this problem? (x-2/4)squared - (y + 2)squared = 1

[@rain51db59]

thank you so much!

[@Dantetherium]

Explains so much better than Khan Academy. Wowza

[@saurabhpant8839]

awesome , it is the complete sense . thanks for this sir...

[@brianmclogan]

you are very welcome!

[@jennagibilisco11]

you're an awesome teach this is a huge help! Thank you!

[@brianmclogan]

+Jenna Gibilisco you are very welcome! happy to be able to help!

[@cozyliving6]

so the difference between hyperbolas and ellipses is the (-) in between the x and y fractions ,if i may say and hyperbolas have their foci and vertices added and subtracted to the left that is at h?while for ellipses we add and subtract at k?

[@brianmclogan]

yes, same processes, just that the vertices are inside of the foci for a hyperbola

[@jahnachyreen8567]

Who's here because of online class? HAHA

[@joshualee5766]

learned more from him than in my online class tbh

[@lovelyjoyarapocvillare2046]

Umaayyy sakit na ulo ko😭

[@kittycat3312]

Me! Learning more from him and professor Leonard than my class T.T I like Prof. Leonard's slower pacing for learning the first time. But this faster one is nice for reviewing material.

[@kristinefernandez8290]

mama mo

[@fed_eric]

Me: raises right hand. 🖐

[@weechacha]

u are a savior !

[@Ashi2779]

Thank You!

[@haroldjanbesario6433]

Shouldn't y=1/2x -3/2 be y=-1/2x - 1/2? Just Wondering if I'm wrong or not

[@mehrandom4056]

Just want to say thanks man

[@krystellelrn]

what if the value of a under y is lesser than the value of b under x???

[@sukhrajsingh9748]

i had the same problem i needed to solve so this helps out a lot

[@mspeneney]

Thank you sir 😃😭👍🏻🙏. Amen to you..

[@brennanferris7400]

God I wish my teacher taught like this. She over complicated everything. Thanks for the help!

[@brianmclogan]

+Brennan Ferris you are very welcome! happy to help

[@nissanjoshi2326]

it seems it would always an hyperbola with horizontal transverse axis since 'x' always appears over 'a' or what sir plz explain

[@biancablake1999]

you know if x is over a when x is over the bigger number.

[@biancablake1999]

oh i just realized that was 2 years ago so that test probably happened 2 years ago as well oops

[@ineedurattention2396]

6:24 where did the number 2 go? Was it multiplied or divided? Cancelled out? Please kindly explain sir

[@catdog8858]

He just moved it infront of the other numbers I think

[@jacklewarne5025]

Isn’t it horizontal if is y first and vertical if it’s x

[@catdog8858]

Why when he puts in h and k into the asymptote formula he puts negative 2, not positive 2??

[@ttorumas]

So would the covertices of this be (1,-1) and (1,-3)?

[@brianmclogan]

sounds right

[@WolfsRainInuyasha101]

Amazing video !!!! I Thank you

[@brianmclogan]

WolfsRainInuyasha101 you are very welcome! happy to help

[@alexandonov8253]

I don’t think your students know how lucky they are to have you as their teacher.😩

[@dfhs1765]

What of if the a and b are equal

[@vanessathenot4376]

You are the reason why KZbin exists

[@razasyed575]

We love you Brian McLogan

[@markmartinodiongan740]

Isnt it vertical tranverse axis?

[@coltonbradley4239]

my man saving my pre cal grade

[@tangahin3263]

Where did he get - 1/2 at 7:40

[@ahmedabdelmaaboud3460]

Why C= a^2 +b^2 Not a^2-b^2?

[@gameforest9360]

Most I've ever learned about hyperbolas in my entire life

[@SnehlataSharma]

Nice

[@newbiedrunkdriver9293]

That c~~ 🎶 was beautiful lol

[@joeg3246]

at 4:27, you drew the focus at approx (4.25,0), shouldn't the Focus end up being approx 2.23 from the center instead of the sum of 1+/- Sq rt 5 (3.23) from the center? Thanks for the videos!

[@joeg3246]

i meant (4.25,-2)

[@brianmclogan]

Since I am estimating and not using exact values, everything can be a little off. The square root of 5 is approximately 2.23. We need to travel that distance from the center which is (1,-2) By adding and subtracting 2.23 we would have points (3.23,-2) and (-1.23,-2). It seems I was adding an extra one but you are absolutely correct. The focus will be right next to the vertices

[@sebastiann.a.g.7528]

HAHAHAHAHA I am about to comment that as well until I found this 😍😘

[@cordial-chefS]

You r great

[@christyamaranathfernando8212]

What year level are you teaching?

[@brianmclogan]

Pre-cal or Algebra 2, do not remember which

[@cynthiamupanda405]

awesome video.THANK YOU.

[@brianmclogan]

Cynthia mupanda you are very welcome! happy to be able to help you out!

[@sheastanford6260]

you saved me!!!

[@brianmclogan]

shea stanford you are very welcome! happy to be able to help you out!

[@summerevans5301]

3:24 Professor McLogan's deathstare 10/10

[@hughjassole7600]

i like this bald guy hes better than most of my professors

[@brianmclogan]

hugh Jassole it's shaved! but thank you : )

[@joyhyun9994]

at 4:23 you meant foci, right?

[@brianmclogan]

+Jihoo A. (Dragonbro) correct

[@redevlmao]

3:23 had beautiful pitch

[@babarmurtaza7765]

eccentricity of hyperbola (x^2/a^2)+(y^2/b^2)=1 Please reply as early as possible,i have an incoming test

[@babarmurtaza7765]

The eccentricity should be in terms of a and b,what would it be,Sir?

[@brianmclogan]

that is not the equation of a hyperbola and eccentricity is =c/a

[@imxxnamv886]

man, this really saves my ass

[@MegaNightZeroX]

What is a asymptotes?

[@brianmclogan]

I have a video for that. It is basically a value that a function cannot be evaluated for but rather approach. For instance f(x)= 1/x Keep plugging in numbers for x and what you is see that the functions gets really close(approaches) but can never equal zero

[@user-zn7by7bj3v]

ي ليت فيه ترجمههه

[@Bellaexe5091]

*me watching this because my teacher is horrific at teaching*

[@Ryangbob]

Minute 3:23 best moment look at his face

[@brianmclogan]

hahaha

[@taliawillson6687]

4:13 I think he meant to say the square root of 9 is 3

[@juan.2001]

Honestly why am I going to math class like I learn the same stuff in 10 minutes here versus 50 minutes in class

[@hussainaladwan7902]

4:10 did he really just say the square root of 3 is 9? bruhhhhh this dude got me trippin

[@brianmclogan]

sorry about that, thanks for keeping me honest

[@hussainaladwan7902]

Brian McLogan haha no problem. Thanks for all ur math vids, they really help.

[@brianmclogan]

you are very welcome Hussain

[@keithrichards9034]

Axis : Bold As Live

[@brianmclogan]

+Keith Richards yes?

[@keithrichards9034]

Mr. McLogan's Math Channel*Axis : Bold As Love

[@keithrichards9034]

Mr. McLogan's Math Channel It must be about maths...

[@chadfoy290]

7:53-8:02 -1.5 - 2 is -3.5

[@al-jamebalina5339]

Did you regret, going to STEM strand?

[@deryavarc183]

3.25 what's happening 😂😂

[@officialdeathbyrainbow8683]

math final prep time the day of 30 mins before

[@littledeathmark8991]

Why won't anyone notice him saying "Vertice" as the singular of "Vertices", it's vertex :3

[@hannahbee2908]

cause its not that deep, we have what is called "common sense"

[@littledeathmark8991]

@@hannahbee2908 Well, I have my pride and you have your so called "Common Sense" which doesn't help in all times

[@Krissypooh0212]

It's supposed to be a(^2) minus b(^2) and not addition

[@brianmclogan]

+Nit Sirk for an ellipse you are correct, for a hyperbola it is a^2 +b^2

[@bluemarshmallowgamer5507]

isn't it suppose to be a over b not b over a?

[@brianmclogan]

this has a horizontal transverse axis so it is b over a, a vertical transverse axis is a/b

[@ttorumas]

BlueMarshmallowGamer Brian McLogan I remember it by ABdomen for vertical since your abdomen runs up/down your body, and BArcode for horizontal since both go left/right

[@ameliepare6062]

3:25 🤣🤣🤣

[@Nicole-tu4tq]

3:30 LMAO

[@brianmclogan]

🙌💪

[@vfxentity]

i would fail the exam if i actually decided to read the book

[@brianmclogan]

Don’t do that

[@HeyKevinYT]

0:16 mmmmm

[@gabrielganzaga365]

are you a fo-s-eye person or a foki person?

[@mythl2179]

so POGGSAHAHAH

[@kitman2152]

you are my dad

[@marymaelibratar5371]

Kalbo