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
Пікірлер: 260
Shout out to brian for making my grade go from a 73 to a 94 in pre-cal. These videos are a NECESSITY
@brianmclogan
7 жыл бұрын
Happy to be able to help you out, keep up the hard work
@christina-mz1lp
9 ай бұрын
I’m trying precalc so hard :(
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
5 жыл бұрын
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
Жыл бұрын
Thanks so much for this video
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
I wonder why majority of the people in this world cannot appreciate the beauty of math, keep it up sir
@jasonyntig717
3 жыл бұрын
It’s just so hard... but I do appreciate the beauty of literature
@BOSS-nz2hw
3 жыл бұрын
Becasue teachers are not letting us appreciate it. Just Stating facts
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
5 жыл бұрын
yes I have plenty of calc videos, hoping to make more
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!
Forever wishing you were my pre-calc teacher👌🏼 Learned so much from you!
@brianmclogan
7 жыл бұрын
awesome! happy to be able to help you out
@hoshimiazami18
6 жыл бұрын
Madeleine Kreger yeah me too
i like the fact that i feel like im in class ,when watching your videos .
@brianmclogan
7 жыл бұрын
I like that too
@irehman7
5 жыл бұрын
Then why don't you pay attention in class and come here watch XD.....just kidding
im from nigeria and youre a blessing youve saved my gpaa!
@brianmclogan
7 жыл бұрын
happy to be able to help you out, all the way in nigeria
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 :)
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
9 жыл бұрын
BasketballPownage thank you, very happy to be able to make a difference
i just recently found your videos and honestly its keeping me afloat in precalc these are really helpful
bro u are better than my teacher in room LOL ...I understand a lot thank you bro this really help me ^.^
@brianmclogan
6 жыл бұрын
awesome! happy to help
@raziljaycamariosa7476
6 жыл бұрын
same as here hahahaha
Thank you so much, this helped me a ton! The way you teach is super easy to understand, please keep making videos :)
@brianmclogan
9 жыл бұрын
Merina Simone thank you very much for your kind words, happy to keep making videos
Thank you so much! My math teacher makes connections that I can't yet, so your videos really round it out.
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.
this was a hyperbola, you put the foci on the wrong spots. Other than that good video
@brianmclogan
7 жыл бұрын
good catch, thanks! I will update on the video
@keenanweind1780
5 жыл бұрын
I was about to put the same reply, you beat me to it...
@jamesruwe5566
5 жыл бұрын
a^2-b^2=c^2
@carlmina4287
5 жыл бұрын
@@jamesruwe5566 no, on hyperbola its addition bruv
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
6 жыл бұрын
you are very welcome Glenn! Wish you the best of luck!
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
9 жыл бұрын
STONEAJE awesome! that is why I post them for students like you. happy to be there to help
You just save me from failing my quiz! I think I learn more watching your video tutorial than listening to my pre-cal teacher...
I’m an expat living in Saudi Arabia and your videos really do help! Thanks!
you are welcome!
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
3 жыл бұрын
So happy to help!!
@ranjithraj36
3 жыл бұрын
@@brianmclogan 🙏🙏sir 😊😊
Absolutely You are awesome ! I see you as my maths teacher. Respect from ethiopia.
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
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
7 жыл бұрын
great job Ryan! I am happy to have been able to help you and see your hard work pay off
@ryanjayreyes7019
7 жыл бұрын
+Brian McLogan Yeah! You can count on it..😊😊 Hope you still continue to upload videos
@brianmclogan
7 жыл бұрын
ohhh yes
can you make a tutorial on how to get the latera recta of hyperbola?
shout out to Brian from Melbourne, Australia. Your videos are very helpful.
@brianmclogan
6 жыл бұрын
cheers! glad they work for you
I am the 100th Viewer! Thanks so much for helping me with math, I wish my teacher was like you.
This helps so much! thank you
jesus these vids help so much thanks Brian
@brianmclogan
7 жыл бұрын
you are very welcome!
This guy is carrying me through my classes
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
6 жыл бұрын
you are very welcome and happy to be able to help
@1121jitseng
6 жыл бұрын
Can sir do more discussion on stpm maths level?
who ever doesn't raise their hand to ask a question must sit in the corner wearing a dunce cap!
@brianmclogan
7 жыл бұрын
agreed
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
7 жыл бұрын
A and B are the coefficients of x and y squared.
your students have a remarkable ability to ask the questions exactly as i think them in my head
@brianmclogan
6 жыл бұрын
that's awesome!
Great video. Thank you
you are very welcome! Go Detroit
This vid is so helpful to recall my knowledge about this. I don't understand what i wrote on my notes xD. Thanks sir!
really out here saving my algebra II grade like that
from Kenya your videos are very awesome thank you
@brianmclogan
6 жыл бұрын
that is awesome! happy to be able to help you out!
Thank you very much. This really helped a lot. :) keep it up.
@brianmclogan
9 жыл бұрын
John Patrick Clemente will do
this is a blessing
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.
sir , i learned so much from your videos .. thank u
@brianmclogan
6 жыл бұрын
you are very welcome!
Thank you so much! Helped a lot
@brianmclogan
7 жыл бұрын
happy to help
Is it possible to comeup with these asymptotes? 2x+sqrt3y-2=0 and -2x+sqrt3y+2=0
love you man
That class room vibe ♥️
besssssttttt teacherrrrr🥺✨
THANK YOU MR.MCLOGAN!
@brianmclogan
10 жыл бұрын
you are very welcome! happy to help!
THANK YOU THANK YOU THANK YOU!!!
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
5 жыл бұрын
It was created to a perfect square trinomial
Thank you Sir!!!
thank you so much ..you helped me a lot :)
@brianmclogan
8 жыл бұрын
+Farah Hamoudeh you are very welcome! happy to be able to help
Thanks sir you help me alot new subscriber here :D
@brianmclogan
9 жыл бұрын
Jace Cz Alexandersson perfect! happy to have you
you da real MVP
@brianmclogan
8 жыл бұрын
+Jay Arciga just happy to help!
Thanks very much
wow pure genius
How do you when you have xy terms
Where are the foci supposed to be
I'm from Philippines and you sir helped me out. thanks sir
@brianmclogan
7 жыл бұрын
awesome! happy to be able to do so. Keep up the hard work
@sadgurusachhivani7171
6 жыл бұрын
really helpful but one problem is that letters are nt clear
The method that he used in the beginning is that completing the square?
@brianmclogan
6 жыл бұрын
yes
Mashallh very good work
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.
I got test tomorrow and this video saved me.
@brianmclogan
6 жыл бұрын
awesome, best of luck Josue!
You're so nice that you don't get irritated with the dumb questions those kids be asking haha
@brianmclogan
7 жыл бұрын
I am just trying to do my part to help, I was once in those shoes
wow these are some legendary comments Im taking pre calc right now I wonder where all these people are at in their lives now.
Wish you could be my pre-cal teacher. I do understand the way you discuss.
@brianmclogan
6 жыл бұрын
Happy to help! I have plenty more videos to come
but what was the mustang news?
Can you teach integration and calculus too? Would mean a lot. Amazing videos thou.
@brianmclogan
6 жыл бұрын
"#integration mclogan" give it a search, plenty of videos. Thanks
@momalzahid4577
6 жыл бұрын
Brian McLogan Thanks a lot. Keep guiding us.
@brianmclogan
6 жыл бұрын
always😀
thank you
Very helpful!!!
@brianmclogan
9 жыл бұрын
Fardin Islam perfect! happy to help
Amazing!
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
5 жыл бұрын
happy to be able to help you out!
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
7 жыл бұрын
divide it out so that the (x-2)^2 is isolated
@speciesunspecified2199
7 жыл бұрын
Brian McLogan how can I divide it when there's already a denominator? And do I have to divide the other variable too?
How do you know which equation to use ???
@brianmclogan
7 жыл бұрын
I hope this helps kzread.info/dash/bejne/h3l1lc2cYtCZhbQ.html
Another great video. Don't lose patience with your students. You're good at this, but it's their first time seeing this.
@brianmclogan
6 жыл бұрын
Sometimes, sometimes a video I make is the 5th time they have seen it, however point well taken
Is that one example of general equation of hyperbola?
@brianmclogan
6 жыл бұрын
yes
Thanks bruh!
@brianmclogan
10 жыл бұрын
you very welcome!TheVegetableAddict
this dude really approximated the square root of 7 on the spot, wow
ngl this be helping me in 2020 XD
How do you identify the center pleas i have test tomorrow???😭😭
Mid-term exams tomorrow. pray for me!
still coming in clutch
Nice sir
solid lods
Those students who doesn't know how to raise their hand before asking a question. UGH!!! 😫😫
@brianmclogan
6 жыл бұрын
haha seriously, I will take blame for allowing it
7:50 brian mclogan snapped
How dafaq did you get the 2x ! You didn't explain it
what is the focus in an ellipse? please help
@brianmclogan
7 жыл бұрын
an ellipse has two foci, they lie on the major axis and have a distance of c from the center
@imeprezime1285
3 жыл бұрын
@@brianmclogan And what are TWO most important properties of these two points in an ellipse?
I'm from egypt master Where are you from
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
is this video from school or the tuitions you take after the school?
@brianmclogan
8 жыл бұрын
+nidhish gautam during school, but I also record after school and during the summer
what happened with the 2x at 2:00?
@brianmclogan
9 жыл бұрын
KinsGlory I completed the square
@KinsGlory
9 жыл бұрын
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.
hoping someday u can teach me how to solve hyperbola
@brianmclogan
6 жыл бұрын
WHAT DO YOU MEAN "SOLVE HYPERBOLA"
@akisahmarmaya7368
6 жыл бұрын
what i mean is solving because im really weak in math
What if you’re given (y-4)squared=-12x
@brianmclogan
6 жыл бұрын
then you do not have to complete the square, I have plenty of videos similar
0:19 there's nothing terrible there though
how is square root of 7 3.65???
@brianmclogan
8 жыл бұрын
+Erik Pogosyan it is not it is approximately 3.65
Can someone help me with this? thank you. The graph of y = −x4 + 12x − 18 (A) intersects the x-axis at exactly one point. (B) intersects the x-axis at exactly two points. (C) intersects the x-axis at exactly three points. (D) intersects the x-axis at exactly four points. (E) does not intersect the x-axis.
@brianmclogan
5 жыл бұрын
Sorry I am unable to focus on problems outside of class but hopefully someone can help
@fairoozzahin4414
5 жыл бұрын
Not nice for a teacher but thanks anyway
@brianmclogan
5 жыл бұрын
not nice? I do what I can to help but there is simply not enough time in the day for me to answer specific questions I receive every day. I hope you would understand that
@fairoozzahin4414
5 жыл бұрын
Now hold on...you have the time to reply to a video over 5 years old but you don't have time to even bother reading the question seeing if it's possible to help. Why the heck would I ask if I wasn't soo desperate because I don't have anyone to ask . But no... go back to your business. This is the condition of things half way around the world. So much for asking for HeLp...LMAO BYE
@brianmclogan
5 жыл бұрын
I did read your question, and was unable to determine a quick answer that I could provide. I try to help as much I can but do received a lot of questions and just simply unable to help everyone that has a question.