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
B/A would be 1/2 not 1/4
@brianmclogan
6 жыл бұрын
yes Elisabeth! great catch! I have pinned your comment so others are not confused
@katiem8025
5 жыл бұрын
He fixed it in the video
@pat1373
3 жыл бұрын
@Chris Abram 🧢, it's probably a sight where you gotta pay or download xyz games
3:23 lmao at whoever sang the "c"
@dj2kbased
5 жыл бұрын
LMAOOOO 😂😂😂😂
@powell3463
4 жыл бұрын
He sang a 'G' actually
@benbillings3237
4 жыл бұрын
Jay Wu ah but fuck u tho
@benbillings3237
4 жыл бұрын
Jay Wu just watch the math
@scarlethart7857
4 жыл бұрын
I don't think you know what that means...
3:21 he gave that man who started singing the death stare lmaooo
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
9 жыл бұрын
Jd Mender you are very welcome! happy to be able to help you out!
@syandaemanuel1342
6 жыл бұрын
Jd Mender same to me,its woow
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
Жыл бұрын
Me too! I was looking for someone to talk about it 😂
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
6 жыл бұрын
you are very welcome! happy to be able to help you out!
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
6 жыл бұрын
you are very welcome! happy to be able to help!
....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!
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
God's gift to man! Studying before my final and this refresher was just what the doctor ordered!
@brianmclogan
2 жыл бұрын
Perfect!!
Thank You!! This makes complete sense FINALLY!
I know I can always rely on your videos, sir!! Thank you very much 💖💖
@brianmclogan
2 жыл бұрын
You are very welcome!!
at 3:23 best part
@brianmclogan
9 жыл бұрын
Ayan Behjat haha funny
@SinjidKhan
8 жыл бұрын
+Ayan Behjat Then Mr. McLogan's reaction, haha.
@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
7 жыл бұрын
Damn bro, you just brought me to the past. It's been almost a year.
@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
you better! good luck and let me know how you do
Great explanation! Thank you!
thank you birria brian you carry me so much during precalc you will always have my blessing
Getting me through pre-cal man, you're a life saver
Your video made me pass my precal! Thank you for this!!:)
Thank you sir, this helped me a lot.
will have midterm exams in pre-calc next week. thank you for this. wish me luck!
All this coughing gonna get me infected thru my phone in 2020
3:22 XDD He was about to smack the shit outta him.
@brianmclogan
8 жыл бұрын
no, would never do that
@raultorres847
8 жыл бұрын
hahaha I saw it and I went right to the comments
@westsidenikkaboi4090
7 жыл бұрын
Brian McLogan he was joking
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
8 жыл бұрын
+Hunter Mill that is great to hear Hunter, pleased to be able to assist you this year
Thanks,,cuz I was very much confused in this particular eqn. 👌🏻
Brian McLogan your straightforward explanations are terrific. Brian McLogan is the McMan. /Regards
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
omg genius man!!!! ty sooo much i have a quiz tomorrow!!!! hope i remebemer!!!
You sir, are a blessing
Thank you sir, you are one of the reason why i survive my math subjects, your making it easy for me💓
Thank you! This was Really helpful!
@brianmclogan
8 жыл бұрын
+Urmi Patel sweet, glad I could help you!
You are a legend. Was stuck on an asymptote forever and this got it in like 2 seconds!
I don’t think your students know how lucky they are to have you as their teacher.😩
Shouldn't y=1/2x -3/2 be y=-1/2x - 1/2? Just Wondering if I'm wrong or not
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
5 жыл бұрын
yes, same processes, just that the vertices are inside of the foci for a hyperbola
Explains so much better than Khan Academy. Wowza
Great teacher... ❤
I actually try it first and recorrecting by watching your equation and guest what... we've matched up. Thanks
Year 2021 and the math never changes .... thanks teacher
thank you so much!
how to solve this problem? (x-2/4)squared - (y + 2)squared = 1
u are a savior !
You are the reason why KZread exists
6:24 where did the number 2 go? Was it multiplied or divided? Cancelled out? Please kindly explain sir
@catdog8858
3 жыл бұрын
He just moved it infront of the other numbers I think
Thank You!
what if the value of a under y is lesser than the value of b under x???
it seems it would always an hyperbola with horizontal transverse axis since 'x' always appears over 'a' or what sir plz explain
@biancablake1999
7 жыл бұрын
you know if x is over a when x is over the bigger number.
@biancablake1999
7 жыл бұрын
oh i just realized that was 2 years ago so that test probably happened 2 years ago as well oops
you're an awesome teach this is a huge help! Thank you!
@brianmclogan
8 жыл бұрын
+Jenna Gibilisco you are very welcome! happy to be able to help!
We love you Brian McLogan
Why when he puts in h and k into the asymptote formula he puts negative 2, not positive 2??
Just want to say thanks man
awesome , it is the complete sense . thanks for this sir...
@brianmclogan
7 жыл бұрын
you are very welcome!
So would the covertices of this be (1,-1) and (1,-3)?
@brianmclogan
5 жыл бұрын
sounds right
Thank you sir 😃😭👍🏻🙏. Amen to you..
Isn’t it horizontal if is y first and vertical if it’s x
i had the same problem i needed to solve so this helps out a lot
my man saving my pre cal grade
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
10 жыл бұрын
i meant (4.25,-2)
@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
5 жыл бұрын
HAHAHAHAHA I am about to comment that as well until I found this 😍😘
Who's here because of online class? HAHA
@joshualee5766
3 жыл бұрын
learned more from him than in my online class tbh
@lovelyjoyarapocvillare2046
3 жыл бұрын
Umaayyy sakit na ulo ko😭
@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
2 жыл бұрын
mama mo
@fed_eric
2 жыл бұрын
Me: raises right hand. 🖐
Amazing video !!!! I Thank you
@brianmclogan
9 жыл бұрын
WolfsRainInuyasha101 you are very welcome! happy to help
God I wish my teacher taught like this. She over complicated everything. Thanks for the help!
@brianmclogan
8 жыл бұрын
+Brennan Ferris you are very welcome! happy to help
Most I've ever learned about hyperbolas in my entire life
Nice
What of if the a and b are equal
Isnt it vertical tranverse axis?
What year level are you teaching?
@brianmclogan
5 жыл бұрын
Pre-cal or Algebra 2, do not remember which
That c~~ 🎶 was beautiful lol
Why C= a^2 +b^2 Not a^2-b^2?
You r great
3:24 Professor McLogan's deathstare 10/10
awesome video.THANK YOU.
@brianmclogan
9 жыл бұрын
Cynthia mupanda you are very welcome! happy to be able to help you out!
Where did he get - 1/2 at 7:40
*me watching this because my teacher is horrific at teaching*
i like this bald guy hes better than most of my professors
@brianmclogan
9 жыл бұрын
hugh Jassole it's shaved! but thank you : )
at 4:23 you meant foci, right?
@brianmclogan
8 жыл бұрын
+Jihoo A. (Dragonbro) correct
3:23 had beautiful pitch
you saved me!!!
@brianmclogan
9 жыл бұрын
shea stanford you are very welcome! happy to be able to help you out!
eccentricity of hyperbola (x^2/a^2)+(y^2/b^2)=1 Please reply as early as possible,i have an incoming test
@babarmurtaza7765
6 жыл бұрын
The eccentricity should be in terms of a and b,what would it be,Sir?
@brianmclogan
6 жыл бұрын
that is not the equation of a hyperbola and eccentricity is =c/a
4:13 I think he meant to say the square root of 9 is 3
man, this really saves my ass
Honestly why am I going to math class like I learn the same stuff in 10 minutes here versus 50 minutes in class
Minute 3:23 best moment look at his face
@brianmclogan
6 жыл бұрын
hahaha
7:53-8:02 -1.5 - 2 is -3.5
ي ليت فيه ترجمههه
Did you regret, going to STEM strand?
What is a asymptotes?
@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
4:10 did he really just say the square root of 3 is 9? bruhhhhh this dude got me trippin
@brianmclogan
6 жыл бұрын
sorry about that, thanks for keeping me honest
@hussainaladwan7902
6 жыл бұрын
Brian McLogan haha no problem. Thanks for all ur math vids, they really help.
@brianmclogan
6 жыл бұрын
you are very welcome Hussain
math final prep time the day of 30 mins before
Axis : Bold As Live
@brianmclogan
8 жыл бұрын
+Keith Richards yes?
@keithrichards9034
8 жыл бұрын
Mr. McLogan's Math Channel*Axis : Bold As Love
@keithrichards9034
8 жыл бұрын
Mr. McLogan's Math Channel It must be about maths...
Why won't anyone notice him saying "Vertice" as the singular of "Vertices", it's vertex :3
@hannahbee2908
3 жыл бұрын
cause its not that deep, we have what is called "common sense"
@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
It's supposed to be a(^2) minus b(^2) and not addition
@brianmclogan
8 жыл бұрын
+Nit Sirk for an ellipse you are correct, for a hyperbola it is a^2 +b^2
3.25 what's happening 😂😂
you are my dad
3:25 🤣🤣🤣
isn't it suppose to be a over b not b over a?
@brianmclogan
6 жыл бұрын
this has a horizontal transverse axis so it is b over a, a vertical transverse axis is a/b
@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
3:30 LMAO
@brianmclogan
Жыл бұрын
🙌💪
0:16 mmmmm
i would fail the exam if i actually decided to read the book
@brianmclogan
Жыл бұрын
Don’t do that
so POGGSAHAHAH
Kalbo
are you a fo-s-eye person or a foki person?