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

Пікірлер: 188

  • @elisabethmaldonado9111
    @elisabethmaldonado91116 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

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

  • @katiem8025

    @katiem8025

    5 жыл бұрын

    He fixed it in the video

  • @pat1373

    @pat1373

    3 жыл бұрын

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

  • @scottyscott7587
    @scottyscott75875 жыл бұрын

    3:23 lmao at whoever sang the "c"

  • @dj2kbased

    @dj2kbased

    5 жыл бұрын

    LMAOOOO 😂😂😂😂

  • @powell3463

    @powell3463

    4 жыл бұрын

    He sang a 'G' actually

  • @benbillings3237

    @benbillings3237

    4 жыл бұрын

    Jay Wu ah but fuck u tho

  • @benbillings3237

    @benbillings3237

    4 жыл бұрын

    Jay Wu just watch the math

  • @scarlethart7857

    @scarlethart7857

    4 жыл бұрын

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

  • @franman6076
    @franman60763 жыл бұрын

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

  • @jdmender3128
    @jdmender31289 жыл бұрын

    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

    @brianmclogan

    9 жыл бұрын

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

  • @syandaemanuel1342

    @syandaemanuel1342

    6 жыл бұрын

    Jd Mender same to me,its woow

  • @DevastatorXD03
    @DevastatorXD032 жыл бұрын

    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

    @ThatweirdEMTnerd

    Жыл бұрын

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

  • @BuZGaming
    @BuZGaming6 жыл бұрын

    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

    @brianmclogan

    6 жыл бұрын

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

  • @nanasparkl3
    @nanasparkl36 жыл бұрын

    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

    @brianmclogan

    6 жыл бұрын

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

  • @doomslayer3294
    @doomslayer32944 жыл бұрын

    ....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!

  • @gavinmatsu
    @gavinmatsu5 жыл бұрын

    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

  • @zachstarattack7320
    @zachstarattack73202 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    2 жыл бұрын

    Perfect!!

  • @strongandhealthy1111
    @strongandhealthy11119 жыл бұрын

    Thank You!! This makes complete sense FINALLY!

  • @mikyllaguigayoma8241
    @mikyllaguigayoma82412 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    2 жыл бұрын

    You are very welcome!!

  • @ayanbehjat4265
    @ayanbehjat42659 жыл бұрын

    at 3:23 best part

  • @brianmclogan

    @brianmclogan

    9 жыл бұрын

    Ayan Behjat haha funny

  • @SinjidKhan

    @SinjidKhan

    8 жыл бұрын

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

  • @indefinite115

    @indefinite115

    7 жыл бұрын

    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

    @SinjidKhan

    7 жыл бұрын

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

  • @indefinite115

    @indefinite115

    7 жыл бұрын

    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

  • @brianmclogan
    @brianmclogan10 жыл бұрын

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

  • @sue-sageasmr2020
    @sue-sageasmr20205 жыл бұрын

    Great explanation! Thank you!

  • @justinsin9423
    @justinsin94232 жыл бұрын

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

  • @JeeterMCHeater
    @JeeterMCHeater7 ай бұрын

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

  • @iceicebaby_09
    @iceicebaby_092 жыл бұрын

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

  • @al-jamebalina5339
    @al-jamebalina53393 жыл бұрын

    Thank you sir, this helped me a lot.

  • @somethingsomewhere509
    @somethingsomewhere5093 жыл бұрын

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

  • @azuurasmr7937
    @azuurasmr79374 жыл бұрын

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

  • @kwame1015
    @kwame10158 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    no, would never do that

  • @raultorres847

    @raultorres847

    8 жыл бұрын

    hahaha I saw it and I went right to the comments

  • @westsidenikkaboi4090

    @westsidenikkaboi4090

    7 жыл бұрын

    Brian McLogan he was joking

  • @LedCODprductions
    @LedCODprductions8 жыл бұрын

    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

    @brianmclogan

    8 жыл бұрын

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

  • @amanlrwtfsm1323
    @amanlrwtfsm13235 жыл бұрын

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

  • @GeoCalifornian
    @GeoCalifornian5 жыл бұрын

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

  • @fishsticks3729
    @fishsticks37293 жыл бұрын

    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

  • @tashasolorzano8545
    @tashasolorzano854510 жыл бұрын

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

  • @jeffreyhernandez9682
    @jeffreyhernandez96825 жыл бұрын

    You sir, are a blessing

  • @FaroukHussienSaripBSarip
    @FaroukHussienSaripBSarip3 жыл бұрын

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

  • @urmisoneji5719
    @urmisoneji57198 жыл бұрын

    Thank you! This was Really helpful!

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +Urmi Patel sweet, glad I could help you!

  • @slashmaster7690
    @slashmaster76904 жыл бұрын

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

  • @alexandonov8253
    @alexandonov82534 жыл бұрын

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

  • @haroldjanbesario6433
    @haroldjanbesario64334 жыл бұрын

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

  • @cozyliving6
    @cozyliving65 жыл бұрын

    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

    @brianmclogan

    5 жыл бұрын

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

  • @Dantetherium
    @Dantetherium5 жыл бұрын

    Explains so much better than Khan Academy. Wowza

  • @muzamilmahtab5588
    @muzamilmahtab55884 жыл бұрын

    Great teacher... ❤

  • @paulsigalat9646
    @paulsigalat96462 жыл бұрын

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

  • @ezrayitbarek2875
    @ezrayitbarek28753 жыл бұрын

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

  • @rain51db59
    @rain51db593 жыл бұрын

    thank you so much!

  • @KeziahAyala
    @KeziahAyala5 жыл бұрын

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

  • @weechacha
    @weechacha2 жыл бұрын

    u are a savior !

  • @vanessathenot4376
    @vanessathenot43764 жыл бұрын

    You are the reason why KZread exists

  • @ineedurattention2396
    @ineedurattention23963 жыл бұрын

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

  • @catdog8858

    @catdog8858

    3 жыл бұрын

    He just moved it infront of the other numbers I think

  • @Ashi2779
    @Ashi27792 жыл бұрын

    Thank You!

  • @krystellelrn
    @krystellelrn3 жыл бұрын

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

  • @nissanjoshi2326
    @nissanjoshi23269 жыл бұрын

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

  • @biancablake1999

    @biancablake1999

    7 жыл бұрын

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

  • @biancablake1999

    @biancablake1999

    7 жыл бұрын

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

  • @jennagibilisco11
    @jennagibilisco118 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

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

  • @razasyed575
    @razasyed5754 жыл бұрын

    We love you Brian McLogan

  • @catdog8858
    @catdog88583 жыл бұрын

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

  • @mehrandom4056
    @mehrandom40562 жыл бұрын

    Just want to say thanks man

  • @saurabhpant8839
    @saurabhpant88397 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    7 жыл бұрын

    you are very welcome!

  • @ttorumas
    @ttorumas5 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    5 жыл бұрын

    sounds right

  • @mspeneney
    @mspeneney4 жыл бұрын

    Thank you sir 😃😭👍🏻🙏. Amen to you..

  • @jacklewarne5025
    @jacklewarne50255 жыл бұрын

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

  • @sukhrajsingh9748
    @sukhrajsingh9748 Жыл бұрын

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

  • @coltonbradley4239
    @coltonbradley42394 жыл бұрын

    my man saving my pre cal grade

  • @joeg3246
    @joeg324610 жыл бұрын

    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

    @joeg3246

    10 жыл бұрын

    i meant (4.25,-2)

  • @brianmclogan

    @brianmclogan

    10 жыл бұрын

    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

    @sebastiann.a.g.7528

    5 жыл бұрын

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

  • @jahnachyreen8567
    @jahnachyreen85673 жыл бұрын

    Who's here because of online class? HAHA

  • @joshualee5766

    @joshualee5766

    3 жыл бұрын

    learned more from him than in my online class tbh

  • @lovelyjoyarapocvillare2046

    @lovelyjoyarapocvillare2046

    3 жыл бұрын

    Umaayyy sakit na ulo ko😭

  • @kittycat3312

    @kittycat3312

    2 жыл бұрын

    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

    @kristinefernandez8290

    2 жыл бұрын

    mama mo

  • @fed_eric

    @fed_eric

    2 жыл бұрын

    Me: raises right hand. 🖐

  • @WolfsRainInuyasha101
    @WolfsRainInuyasha1019 жыл бұрын

    Amazing video !!!! I Thank you

  • @brianmclogan

    @brianmclogan

    9 жыл бұрын

    WolfsRainInuyasha101 you are very welcome! happy to help

  • @brennanferris7400
    @brennanferris74008 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +Brennan Ferris you are very welcome! happy to help

  • @gameforest9360
    @gameforest9360 Жыл бұрын

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

  • @SnehlataSharma
    @SnehlataSharma6 жыл бұрын

    Nice

  • @dfhs1765
    @dfhs17653 жыл бұрын

    What of if the a and b are equal

  • @markmartinodiongan740
    @markmartinodiongan7403 жыл бұрын

    Isnt it vertical tranverse axis?

  • @christyamaranathfernando8212
    @christyamaranathfernando82125 жыл бұрын

    What year level are you teaching?

  • @brianmclogan

    @brianmclogan

    5 жыл бұрын

    Pre-cal or Algebra 2, do not remember which

  • @newbiedrunkdriver9293
    @newbiedrunkdriver92932 жыл бұрын

    That c~~ 🎶 was beautiful lol

  • @ahmedabdelmaaboud3460
    @ahmedabdelmaaboud34603 жыл бұрын

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

  • @cordial-chefS
    @cordial-chefS10 ай бұрын

    You r great

  • @summerevans5301
    @summerevans53012 жыл бұрын

    3:24 Professor McLogan's deathstare 10/10

  • @cynthiamupanda405
    @cynthiamupanda4059 жыл бұрын

    awesome video.THANK YOU.

  • @brianmclogan

    @brianmclogan

    9 жыл бұрын

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

  • @tangahin3263
    @tangahin32633 жыл бұрын

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

  • @Bellaexe5091
    @Bellaexe50914 жыл бұрын

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

  • @hughjassole7600
    @hughjassole76009 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    9 жыл бұрын

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

  • @joyhyun9994
    @joyhyun99948 жыл бұрын

    at 4:23 you meant foci, right?

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +Jihoo A. (Dragonbro) correct

  • @redevlmao
    @redevlmao2 жыл бұрын

    3:23 had beautiful pitch

  • @sheastanford6260
    @sheastanford62609 жыл бұрын

    you saved me!!!

  • @brianmclogan

    @brianmclogan

    9 жыл бұрын

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

  • @babarmurtaza7765
    @babarmurtaza77656 жыл бұрын

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

  • @babarmurtaza7765

    @babarmurtaza7765

    6 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

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

  • @taliawillson6687
    @taliawillson66873 жыл бұрын

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

  • @imxxnamv886
    @imxxnamv8862 жыл бұрын

    man, this really saves my ass

  • @juan.2001
    @juan.2001 Жыл бұрын

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

  • @Ryangbob
    @Ryangbob6 жыл бұрын

    Minute 3:23 best moment look at his face

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    hahaha

  • @chadfoy290
    @chadfoy2904 жыл бұрын

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

  • @user-zn7by7bj3v
    @user-zn7by7bj3v3 жыл бұрын

    ي ليت فيه ترجمههه

  • @al-jamebalina5339
    @al-jamebalina53393 жыл бұрын

    Did you regret, going to STEM strand?

  • @MegaNightZeroX
    @MegaNightZeroX10 жыл бұрын

    What is a asymptotes?

  • @brianmclogan

    @brianmclogan

    10 жыл бұрын

    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

  • @hussainaladwan7902
    @hussainaladwan79026 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    sorry about that, thanks for keeping me honest

  • @hussainaladwan7902

    @hussainaladwan7902

    6 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

    you are very welcome Hussain

  • @officialdeathbyrainbow8683
    @officialdeathbyrainbow86832 жыл бұрын

    math final prep time the day of 30 mins before

  • @keithrichards9034
    @keithrichards90348 жыл бұрын

    Axis : Bold As Live

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

    +Keith Richards yes?

  • @keithrichards9034

    @keithrichards9034

    8 жыл бұрын

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

  • @keithrichards9034

    @keithrichards9034

    8 жыл бұрын

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

  • @littledeathmark8991
    @littledeathmark89913 жыл бұрын

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

  • @hannahbee2908

    @hannahbee2908

    3 жыл бұрын

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

  • @littledeathmark8991

    @littledeathmark8991

    3 жыл бұрын

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

  • @Krissypooh0212
    @Krissypooh02128 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    8 жыл бұрын

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

  • @deryavarc183
    @deryavarc1837 ай бұрын

    3.25 what's happening 😂😂

  • @kitman2152
    @kitman21522 жыл бұрын

    you are my dad

  • @ameliepare6062
    @ameliepare60623 жыл бұрын

    3:25 🤣🤣🤣

  • @bluemarshmallowgamer5507
    @bluemarshmallowgamer55076 жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    6 жыл бұрын

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

  • @ttorumas

    @ttorumas

    5 жыл бұрын

    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

  • @Nicole-tu4tq
    @Nicole-tu4tq Жыл бұрын

    3:30 LMAO

  • @brianmclogan

    @brianmclogan

    Жыл бұрын

    🙌💪

  • @HeyKevinYT
    @HeyKevinYT5 жыл бұрын

    0:16 mmmmm

  • @vfxentity
    @vfxentity Жыл бұрын

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

  • @brianmclogan

    @brianmclogan

    Жыл бұрын

    Don’t do that

  • @mythl2179
    @mythl21793 жыл бұрын

    so POGGSAHAHAH

  • @marymaelibratar5371
    @marymaelibratar53713 жыл бұрын

    Kalbo

  • @gabrielganzaga365
    @gabrielganzaga3652 жыл бұрын

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