How to find the foci, center and vertices, 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

[@noahpierce5205]

Shout out to brian for making my grade go from a 73 to a 94 in pre-cal. These videos are a NECESSITY

[@brianmclogan]

Happy to be able to help you out, keep up the hard work

[@christina-mz1lp]

I’m trying precalc so hard :(

[@brianmclogan]

AHHHH thank you for catching the mistake. I think I may have been confused working from another ellipse problem and state incorrectly. For a hyperbola the foci are not between the verticies but out side them! Thank you so much for catching this mistake

[@malachibooth2549]

Brian McLogan ty in helping me with my hw and keep making more videos! Btw I think you graphed the foci wrong because the square root of seven is larger than two (the vertices)

[@johnibrahimbabangida-co3sw]

Thanks so much for this video

[@brianmclogan]

thanks, just trying my best to help out students like yourself. Keep up the hard work and let me know how I can help you further

[@tranquilitypeace-quiet-med8225]

I wonder why majority of the people in this world cannot appreciate the beauty of math, keep it up sir

[@jasonyntig717]

It’s just so hard... but I do appreciate the beauty of literature

[@BOSS-nz2hw]

Becasue teachers are not letting us appreciate it. Just Stating facts

[@MrDubs]

I love being able to search ANYTHING math related this semester and having multiples of your videos pop up. Hope your archive of all things great are there for me next semester for my 7:30am calc class.

[@brianmclogan]

yes I have plenty of calc videos, hoping to make more

[@tyhararain7856]

Thank you, thank you, thank you! This is my first year of being homeschooled and the onsite classes only went up to geometry at my schools site. I've been teaching myself Precalc this entire year and it has been the sole cause of all my sleepless nights and grumpy attitude in the morning. Some how ( I have no idea how) I managed to keep up my A in the class but i think waaay too much crying and headaches was put into it. I love math and not understanding it was making me seriously hate it. Thank you soooo much for taking the time to make/edit these videos, they are sooo helpful. I wish i had learned about them much sooner but i will definitely keep watching your videos the last 6 weeks of school i have left!

[@claramutsakanyi3790]

i like the fact that i feel like im in class ,when watching your videos .

[@brianmclogan]

I like that too

[@irehman7]

Then why don't you pay attention in class and come here watch XD.....just kidding

[@madeleinekreger8309]

Forever wishing you were my pre-calc teacher👌🏼 Learned so much from you!

[@brianmclogan]

awesome! happy to be able to help you out

[@hoshimiazami18]

Madeleine Kreger yeah me too

[@themegachan1]

Thank you a lot. I watch your videos every time I have new homework lol... The way you teach is super super easy to understand. Thank you so much :)

[@ikennao5299]

im from nigeria and youre a blessing youve saved my gpaa!

[@brianmclogan]

happy to be able to help you out, all the way in nigeria

[@luxus20]

bro u are better than my teacher in room LOL ...I understand a lot thank you bro this really help me ^.^

[@brianmclogan]

awesome! happy to help

[@raziljaycamariosa7476]

same as here hahahaha

[@BasketballPownage]

I just wanted to thank you so much! I take pre calc and am doing all of it from home and teaching myself. You help by giving a very clear explanation and it feels very similar to a classroom setting. Thanks a lot, you are helping thousands of struggling teens with hw.

[@brianmclogan]

BasketballPownage thank you, very happy to be able to make a difference

[@Jan_ice]

i just recently found your videos and honestly its keeping me afloat in precalc these are really helpful

[@morganjones616]

Thank you so much! My math teacher makes connections that I can't yet, so your videos really round it out.

[@hiyashah2335]

I’m an expat living in Saudi Arabia and your videos really do help! Thanks!

[@GlennEmmanuelPMardo]

Tomorrow is our examination in Pre-Calculus regarding conic sections I've watched all of your videos regarding conic sections and I learned a lot from you. Thank you so soooo much I really admire/appreciate your intelligence in Mathematics God bless you and your family💖🙂

[@brianmclogan]

you are very welcome Glenn! Wish you the best of luck!

[@JasleenKaur-ht5km]

this was a hyperbola, you put the foci on the wrong spots. Other than that good video

[@brianmclogan]

good catch, thanks! I will update on the video

[@keenanweind1780]

I was about to put the same reply, you beat me to it...

[@jamesruwe5566]

a^2-b^2=c^2

[@carlmina4287]

@@jamesruwe5566 no, on hyperbola its addition bruv

[@kalebrizer6829]

i just discovered the channel thanks for the help because my current teacher honestly just doesnt teach this well and most of my class is having trouble.

[@ak-up8fg]

Absolutely You are awesome ! I see you as my maths teacher. Respect from ethiopia.

[@cocoabunny13]

Thank you so much, this helped me a ton! The way you teach is super easy to understand, please keep making videos :)

[@brianmclogan]

Merina Simone thank you very much for your kind words, happy to keep making videos

[@STONEAJE]

I would just like to say thank you for this. You are an awesome teacher. My teacher is great too (this time at least) but she doesn't have her lectures online for me to check after class! These videos have been helping me a ton.

[@brianmclogan]

STONEAJE awesome! that is why I post them for students like you. happy to be there to help

[@ranjithraj36]

Namasthe Sir I'm from india. Actually I takes online tuitions for NRI students your videos helping me alot thank you so much sir

[@brianmclogan]

So happy to help!!

[@ranjithraj36]

@@brianmclogan 🙏🙏sir 😊😊

[@hook8033]

So if a=2 and c=sqrrt of 7 which is 2.65 roughly wouldnt that put the foci on the outside of the vertices not in between? at 8:52

[@ricaprincesstonga712]

You just save me from failing my quiz! I think I learn more watching your video tutorial than listening to my pre-cal teacher...

[@victorgabrielsioson6528]

can you make a tutorial on how to get the latera recta of hyperbola?

[@brianmclogan]

you are welcome!

[@ryanjayreyes7019]

Thank God !! Your a Life saver!! I survived pre cal with high marks because of you..!! Thank you..!! I'm from philippines by the way..😊😊😊

[@brianmclogan]

great job Ryan! I am happy to have been able to help you and see your hard work pay off

[@ryanjayreyes7019]

+Brian McLogan Yeah! You can count on it..😊😊 Hope you still continue to upload videos

[@brianmclogan]

ohhh yes

[@letsgobuffalo19]

This helps so much! thank you

[@michaeldickson36]

your students have a remarkable ability to ask the questions exactly as i think them in my head

[@brianmclogan]

that's awesome!

[@nozzerjuice]

who ever doesn't raise their hand to ask a question must sit in the corner wearing a dunce cap!

[@brianmclogan]

agreed

[@infamousprince88]

how do you determine your a and b values? Because I watched and followed the steps but it looks like my equations were backwards. Not sure why though because my equation looks pretty much the same

[@brianmclogan]

A and B are the coefficients of x and y squared.

[@parhama1388]

shout out to Brian from Melbourne, Australia. Your videos are very helpful.

[@brianmclogan]

cheers! glad they work for you

[@Emma-pv6xd]

really out here saving my algebra II grade like that

[@arjungrover1451]

jesus these vids help so much thanks Brian

[@brianmclogan]

you are very welcome!

[@marklista8221]

This vid is so helpful to recall my knowledge about this. I don't understand what i wrote on my notes xD. Thanks sir!

[@aidengluck261]

This guy is carrying me through my classes

[@1121jitseng]

You're much better than my teacher in lucture class. She just briefly explained to us and gave us lots of exercises. Thank you so much Sir ;)

[@brianmclogan]

you are very welcome and happy to be able to help

[@1121jitseng]

Can sir do more discussion on stpm maths level?

[@AJ-et3vf]

Great video. Thank you

[@itnolongerexists2877]

How do you when you have xy terms

[@killer0200318]

Where are the foci supposed to be

[@MJ-nf5zh]

this is a blessing

[@islamic_diariesbysidra..8466]

sir , i learned so much from your videos .. thank u

[@brianmclogan]

you are very welcome!

[@bryonsegunto8901]

Is it possible to comeup with these asymptotes? 2x+sqrt3y-2=0 and -2x+sqrt3y+2=0

[@johnpatrickclemente547]

Thank you very much. This really helped a lot. :) keep it up.

[@brianmclogan]

John Patrick Clemente will do

[@Boyhoody]

THANK YOU THANK YOU THANK YOU!!!

[@trey6419]

1:52 I don't get where that "1" is coming from.. Why does it suddenly get added to (x²+2x) at 2:00 ?

[@ivanpallino2605]

It was created to a perfect square trinomial

[@kllyjrd]

I am the 100th Viewer! Thanks so much for helping me with math, I wish my teacher was like you.

[@nicolesteinmetz5363]

Thank you so much! Helped a lot

[@brianmclogan]

happy to help

[@gakerenyingi6063]

from Kenya your videos are very awesome thank you

[@brianmclogan]

that is awesome! happy to be able to help you out!

[@brianmclogan]

you are very welcome! Go Detroit

[@abdallahmusleh5613]

love you man

[@deograciascorderoii7299]

Thank you Sir!!!

[@TheSSgator15]

but what was the mustang news?

[@farahhamoudeh1368]

thank you so much ..you helped me a lot :)

[@brianmclogan]

+Farah Hamoudeh you are very welcome! happy to be able to help

[@jakemoody4464]

THANK YOU MR.MCLOGAN!

[@brianmclogan]

you are very welcome! happy to help!

[@pro-films9920]

That class room vibe ♥️

[@jayarciga5880]

you da real MVP

[@brianmclogan]

+Jay Arciga just happy to help!

[@darrell3806]

I'm from Philippines and you sir helped me out. thanks sir

[@brianmclogan]

awesome! happy to be able to do so. Keep up the hard work

[@sadgurusachhivani7171]

really helpful but one problem is that letters are nt clear

[@orggienyasoka2712]

Thanks very much

[@adbeellopez4792]

You're so nice that you don't get irritated with the dumb questions those kids be asking haha

[@brianmclogan]

I am just trying to do my part to help, I was once in those shoes

[@josuedavid6584]

I got test tomorrow and this video saved me.

[@brianmclogan]

awesome, best of luck Josue!

[@bbank5782]

The foci (-1, 0 +/- root 7) has to be further away from the center than the verticies (-1, 0 +/- 2). Root 7 is greater thatn 2.

[@mutinyonline10]

This lesson was a mess! Reminded me of my initial maths teacher this year, managed to change lecturer but stay in the same course and I actually learn things in class now. When it comes to maths it’s all up to the effort you put in and the teacher you have.

[@crissellshey7585]

besssssttttt teacherrrrr🥺✨

[@halwestnoraden3957]

thank you

[@miguelbanana220]

How do you identify the center pleas i have test tomorrow???😭😭

[@ogbechewisdom1621]

wow pure genius

[@chessabelledablo3535]

The method that he used in the beginning is that completing the square?

[@brianmclogan]

yes

[@Problem_Solvedorg]

Amazing!

[@priMoN6]

Very helpful!!!

[@brianmclogan]

Fardin Islam perfect! happy to help

[@revenevren3344]

Wish you could be my pre-cal teacher. I do understand the way you discuss.

[@brianmclogan]

Happy to help! I have plenty more videos to come

[@HossG8]

How do you know which equation to use ???

[@brianmclogan]

I hope this helps kzbin.info/www/bejne/i3akZJ6ZZ9Jmi7M

[@venczchannel]

Thanks sir you help me alot new subscriber here :D

[@brianmclogan]

Jace Cz Alexandersson perfect! happy to have you

[@speciesunspecified2199]

after getting the standard formula, what if there's a value beside (x-h)^2 .... the equation's like this, y^2 / 1 - 3(x-7)^2 / 2 = 1

[@brianmclogan]

divide it out so that the (x-2)^2 is isolated

[@speciesunspecified2199]

Brian McLogan how can I divide it when there's already a denominator? And do I have to divide the other variable too?

[@ryankandy]

wow these are some legendary comments Im taking pre calc right now I wonder where all these people are at in their lives now.

[@magikyle252]

How dafaq did you get the 2x ! You didn't explain it

[@thevegetableaddict4625]

Thanks bruh!

[@brianmclogan]

you very welcome!TheVegetableAddict

[@sanamsanamrani6206]

Mashallh very good work

[@jullianwoodard535]

man my pre-calc teacher an indian lady wit a strong indian accent and idk what shawty be sayin but this saved me thanks fam

[@brianmclogan]

happy to be able to help you out!

[@momalzahid4577]

Can you teach integration and calculus too? Would mean a lot. Amazing videos thou.

[@brianmclogan]

"#integration mclogan" give it a search, plenty of videos. Thanks

[@momalzahid4577]

Brian McLogan Thanks a lot. Keep guiding us.

[@brianmclogan]

always😀

[@Madmun357]

Another great video. Don't lose patience with your students. You're good at this, but it's their first time seeing this.

[@brianmclogan]

Sometimes, sometimes a video I make is the 5th time they have seen it, however point well taken

[@KinsGlory]

what happened with the 2x at 2:00?

[@brianmclogan]

KinsGlory I completed the square

[@KinsGlory]

Mr. McLogan's Math Channel ahh i see. thank you! Helping me study for my placement tests. Do me a favor and tell your hs students to not put it off! The only thing more tedius than taking them is having to re-learn everything two years later.

[@kafflechawds5660]

ngl this be helping me in 2020 XD

[@shelomithpotayre1114]

Is that one example of general equation of hyperbola?

[@brianmclogan]

yes

[@kyleschwartz.]

still coming in clutch

[@SnehlataSharma]

Nice sir

[@star9129]

Mid-term exams tomorrow. pray for me!

[@earldavidbasal8362]

solid lods

[@alfredo19987]

what is the focus in an ellipse? please help

[@brianmclogan]

an ellipse has two foci, they lie on the major axis and have a distance of c from the center

[@imeprezime1285]

@@brianmclogan And what are TWO most important properties of these two points in an ellipse?

[@areyouchoking1471]

Those students who doesn't know how to raise their hand before asking a question. UGH!!! 😫😫

[@brianmclogan]

haha seriously, I will take blame for allowing it

[@georgeferman761]

this dude really approximated the square root of 7 on the spot, wow

[@erikpogosyan7736]

how is square root of 7 3.65???

[@brianmclogan]

+Erik Pogosyan it is not it is approximately 3.65

[@katiecheng6551]

7:50 brian mclogan snapped

[@spencerfitz6023]

What if you’re given (y-4)squared=-12x

[@brianmclogan]

then you do not have to complete the square, I have plenty of videos similar

[@nevergiveup7233]

I'm from egypt master Where are you from

[@akisahmarmaya7368]

hoping someday u can teach me how to solve hyperbola

[@brianmclogan]

WHAT DO YOU MEAN "SOLVE HYPERBOLA"

[@akisahmarmaya7368]

what i mean is solving because im really weak in math

[@nidhishgautam9043]

is this video from school or the tuitions you take after the school?

[@brianmclogan]

+nidhish gautam during school, but I also record after school and during the summer

[@hachisu5288]

Dammit our first quarterly exams are about parabolas, circles, ellipse, and hyperbolas and im just 16 yr old boi Good thing we are allowed to use and check our formulas the thing is it's 1-100 test so a hundred items and im doing the same thing but with different variants and including the standard and generalized form... I'm done with school hahah

[@brianmclogan]

hahaha just our school news

[@KnightzANT]

Do you teach at Mandarin high school in Jax FL? they're also the Mustangs.. !

[@McShat]

isnt the center (0,-1)