How to find the center, foci and vertices of an ellipse

Learn how to graph vertical ellipse which equation is in general form. A vertical ellipse is an ellipse which major axis is vertical. When the equation of an ellipse is written in the general form, we first rewrite it in standard form using completing the square.
After the equation has been rewritten in the standard form, we then graph the vertical ellipse, by first identifing some of the properties of the ellipse including the major radius and the minor radius and the center. These properties enables us to graph the ellipse.
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This man is a legend. He made all these videos years ago knowing the next generation of students would be so confused. What a big brain.

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Holy shi-

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For real 😍📌 He's such a good teacher

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I understood in 13 minutes what took an hour and a half for my teacher to confuse the crap out of me- thank you!!!

[@brianmclogan]

+atlachinides a hahaha happy to help!

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Math isn't that hard, but teachers have to figure out how to fill up an hour of time so they over complicate it.

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Same

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Almost 2020 and still happens

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I hope he never stops doing these videos because they have carried me through all the mathematics I’ve done in high school... thank you soooo much

[@brianmclogan]

you are very welcome! happy to help!

[@hermontadese5808]

sir when u find the foci u made mistake u did not square the b or 4

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I literally missed 4 days of school and learned everything through your videos. I feel confident for my test tomorrow, thanks!

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This has been 5 yrs i hope youre doing well now

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How’d u do on your test?

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@@gamerboi3447 Wow... can't believe it's already been 5 years. Thank you for your comment! I commented this while studying for Algebra 2 in high school, life was so different then. I'm doing great now, graduating college in December & applying to med school. Time flies... I hope you can look back in 5 years and smile too :)

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​@@wadewilson3296 Hahaha not sure but I think I did well, I ended up with an A in the class

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Wow! Your still here after all these years! I’m taking pre-calc in my junior year in high school. I didn’t expect u to respond lol

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When I need a refresher, I always rely on your material. Thank you!

[@brianmclogan]

***** awesome happy to be there for you

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This made my pre-calculus teacher look like an idiot. Great explanation! Thank you!

[@brianmclogan]

Albanian Keeper : ) happy to help!

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I like how you consistently identify the terms; for example the binomial square, perfect square trinomial, quadratic term. That attention to detail in your lecture makes you a great instructor, from my point of view.

[@brianmclogan]

I think that detail is important so glad to hear you appreciate it

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But the only setbacks are his errors that his students saw and corrected. Anyways, he still recovered.

[@brianmclogan]

well the standard form for o an ellipse the center is (h.k) from (x-h)^2+(y-k)^2 note that is only part of the equation

[@insanelymaniac8522]

Thanks :)

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Ridiculously organized and succint! I love that you go back and forth between explaing and doing. Consistently too! Thank you!

[@brianmclogan]

Sandra Ruiz you are very welcome!

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This is such a big help especially during this time of pandemic wherein we are homeschooled, thank you so much for this!

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I have saved multiple videos of yours. They are very helpful. I appreciate that you explain each step in detail.

[@brianmclogan]

Happy to help Angie

[@brianmclogan]

you are very welcome!

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I like how you give out the trens clearly..thank you

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Can’t emphasize enough how grateful I am for your videos. Truly an expert at your craft. Thank you very much.

[@brianmclogan]

you are very welcome!

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I am teaching my students this morning using your example.... Thank you for your teaching

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Thank you, in the sea of aweful math videos out there in the world this one is clear, understandable, and doesn’t waste time. Good job.

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Wow I managed to understand this so quickly. Thank you so much. I’ll probably watch this video again before my test. Thank you!!

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I AM AN INDIAN AND I AM USING HIS TRICKS TO SOLVE THE PAPER AND GET EASY CALCULATIONS BY PRACTICING THEM DAILY FOR JEE MAINS AND JEE ADVANCE ENTRANCE EXAMS THANKS A LOT , THE BRIAN SIR

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and..did you crack it??

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You are a great teacher... Your patience is off the charts.... And the detail is just beautiful....

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Great tutor. Your examples and explanations are truly reliable

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The students are so honest, it is a good thing, In LATAM, many student will just shut up, so much to learn from other styles of learning and class

[@eturbo97]

You're amazing. All your Conic Section videos were golden in helping me review for my math final exam. Your videos are clear and easy to understand.

[@brianmclogan]

thank you happy to have been able to help you along with that section

[@AngelHernandez-nr4oe]

Years will go by, these videos will always be useful lol

[@brianmclogan]

Thanks Angel

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@@brianmclogan still using this video haha

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Yeah even after 11 years

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u posted this 9 years ago!!! Thank you so much!

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I will for ever thank you for expanding your technical expression to the public

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Thank you sir!! From India. I wish we had teachers like you out here who would explain things to us with graphs!!

[@brianmclogan]

happy to be able to help you out!

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IT’S 2021 AND THIS IS HELPING ME AND I BELIEVE THAT THIS WOULD CONTINUE HELPING OTHERS in the future. i’m sorry i didn’t notice i was on all caps and i’m too lazy to start all over again.

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Extremely great presentation and teachers in school mostly neglect the basics. Great explanation tysm😊😊

[@jacobzu6655]

Finals for Winter Quarter coming up next week. I watch your demonstrations after each lecture and it really helps a ton.

[@brianmclogan]

awesome! happy to be able to help

[@GatorFX]

I honestly wish you were my teacher. For three days I couldn't even figure out where to start with ellipses. In 20 minutes, you taught me more than I could've ever thought. Thank you so much.

[@brianmclogan]

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

[@toddjacobs7192]

Mr. McLogan, I have gone back to school since I got hurt as a firefighter/paramedic and now have to find another job. One of the classes I'm required to take is College Algebra. I never pushed myself when I was in high school (29 years ago), and now, I have to learn things that I should have a LONG time ago. It is much more difficult to learn as an adult, actually, strike that, it is much more difficult to remember what you've learned as an adult. I am currently learning about ellipses and saw that we will soon be in hyperbola's. As I sit here and type this, I can't remember right off hand what I just learned regarding parabola's; I guess where I am going at with this is, people, and especially teachers, that take advantage of technology and take the time to instruct and teach with passion and caring make a huge difference in peoples lives. I doubt I would want to go through high school again in this day and age, however, if I did, having a teacher like you is EXACTLY what I would want. Thank you for posting these videos (even though, so far, this is the only one I've watched) and thank you for teaching. I truly hope your students know how lucky they are to have this kind of technology to help them!

[@brianmclogan]

Todd Jacobs Thank you Todd for your very thoughtful post. The reason I started making videos 4 years ago was for people just like you. I have a lot of examples in conic sections so I hope my videos will continue to help you with your studies. I can only imagine trying to remember this stuff after so many years. Keep up the hard work and let me know if there is anything I can do for you.

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Todd Jacobs I know exactly how you feel, I'm a math major as a result of you tube teaching me. I was in school 20 years ago and now. I can't believe how easy this has become!!!The gift of technology!!!

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Thank you, the lesson was great! You made it understandable and simple.

[@moulikchaurasiya8765]

Love from INDIA 🇮🇳 , watching after 6 yrs of video uploaded, best teaching of ellipse problems.....thank you sir

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Oh my god you just saved my honors algebra 2 grade. THANK YOU!!!

[@minfei.]

7 years ago and still helpful. Thank you!

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I'm taking a placement test to get into my calculus class and had completely forgotten everything that I had learned in precal, this helped so much!!!

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this teacher is so good actually

[@user-kw2je5os9i]

Thank you sir, you definitely made this topic clearer for me and I can now go on and tackle my assignment a bit easier. And one question, are you a high school teacher or college professor?

[@brianmclogan]

happy to help, I am a high school teacher

[@vijaysinghchauhan7079]

thank you for making the concept easier to grasp

[@alishasubedi4847]

I didn't understand anything about parabolas and when i try to learn by myself.It was really confusing. But, after watching your videos. I was able to solve all my books problem. Thank You so much. You really have teaching talents. Do you have videos about sequence and series??

[@brianmclogan]

So happy to be able to help you out. I do have some videos on sequences and series but they are not completely organized yet. Here is what I have so far. kzbin.info/aero/PL0G-Nd0V5ZMpiflYOpyZOQpKBA2srOQJC kzbin.info/aero/PL0G-Nd0V5ZMqKBKsP_BOlWxYS2wErmlw7 kzbin.info/aero/PL0G-Nd0V5ZMoIw8OrzDdhAyvtLjaCIZZB kzbin.info/aero/PL0G-Nd0V5ZMpMjQVyzA6cSE5hSAsEcwuc

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Thankyou so much this really helped me out. My teacher is great but i kinda got confused when i was studying by myself so i came and got extra help here! Thankyou Brian McLogan!!

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Wish my math teacher explained stuff this simply. Thanks so much! Your videos are gonna get me to graduation.

[@syimakim9289]

amazing explanation. i wish you were my teacher.

[@jovanmagtoto1682]

thank you for this sir, I now understand how to determine the center and the eccentricity. Our online class is not complete, with this video, I understand more our topic about ellipse.

[@decowmon]

This equation just happened to be the one i was stuck on, felt like i was given private tutoring. Thanks!

[@communistpootisbirb]

Wasn't even taught this in high school… College expected me to know it before I took my math placement test. I completely understood this in the quick 13 minutes (plus a few pauses give or take) this video was. Thank you so much!!!

[@brianmclogan]

you are very welcome!

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You are amazing teacher. This helped me so much in my study computer sciences while i was need a help in general and discrete mathematics. Thank you so much. God bless you

[@brianmclogan]

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

[@richoleeplazo5755]

I want a teacher like this

[@samoliver13]

Thank you soooo much. I have a quiz tomorrow and I was really confused about this section. I spent a hour and a half and my teachers class and didn’t understand a thing. I watch a 13 minute video and understand it. Wish you were a teacher at my school

[@dozeneggs]

Awesome Explanation The other Trick for finding the Centre is to Solving the Differention for x-coffecients and y-coeffecients and you get the Centre (x,y)

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yes, it works!

[@maintainingmasters]

All concepts cleared thankyou

[@hailey2885]

Thank you so much, my teacher is pressuring us to take a test on Monday when a lot of our class was gone for a half of the week and we have three days of make up. This was Thursday’s work which we did not get a lesson on and are expected to know how to do. You have surpassed my teacher in every way

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Sir , it was a very great explaination i have searched for so many videos on this topic and i got your video ......I am your new student from now I am not only watching also understanding the concepts from india

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You're honestly saving my grade for my final!! I was absent this whole chapter and everyone who tried to explain to me or showed me the book it made no sense but this makes perfect sense

[@brianmclogan]

happy to be able to help!

[@bende7583]

Yo did you do good on your final 😂

[@addiqabintsaleem5623]

Last min prepping for Final today for Precalc (college), just intro stuff is on final about parabolas, ellipses, and hyperbolas. You made it simpler in seeing how the formulas we use came to be. Cramming! ughhh thank you!

[@brianmclogan]

you are very welcome! best of luck!

[@GazmG]

You are so much cooler than my math teacher. Hope you can help during finals, which are coming in a few days.... (cries)

[@brianmclogan]

here for you

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I wish you were my math teacher forever, I did understand everything super duper clean! fav💕

[@brianmclogan]

awesome! happy to be able to help you out Angelita!

[@TheMaster47x]

I wish you were my maths teacher.

[@brianmclogan]

TheMaster47x Thanks, here online for all of your needs, let me know if there is anything I can do for you in the future

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I do appreciate your efforts for making videos especially can help to us as students. God bless you

[@shihokyu248]

This days.. Was hilarious to me.. Because of online classes.... And I'm very thankful to you because, you help me in my study.. I really love your videos.. I learned alot.. It easy to understand.... But may I ask where did you get that (1,-6)in the vertices?... Thank you..

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YOU ARE MY LIFESAVER 😭😭😭 saved me from embarrassing myself infront of my class tomorrow

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[@brianmclogan]

awesome! congrats to you, happy to be there for you and keep up the hard work

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What a nice video!!, tomorrow I have the final contest of maths 10. I understood everything. Thank you🇨🇱

[@brianmclogan]

Best of luck!

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From 🇰🇪🇰🇪,,you are great tutor

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Awesome explanation,honestly i have a big problem in Analytic Geometry & i swear if you wear my professor I wouldn't have bad grades thank you a million time...

[@brianmclogan]

you are very welcome! hope my videos help

[@rufflesarts3871]

My teacher depends us to learn this kind of Math from watching youtube videos...and she does not actually teach us anything....she would just say that watch the videos / links that i send in your school app...and she would be giving us hard problems which really bothers me off... I haven't enjoyed my weekend because of her...she would give online quizzes and assignments through the weekend...i have never bond with my family for a very long time...i just wanna say that thanks for your help Brian McLogan, for all your youtube post which has a subject of Math... which is clearly needed for students like me...to understand this types of lesson better....so THANK YOU...im sorry if im so emotional...i just haven't encountered such teacher who do not actually teaches (most of the time) something in class...so THANKS FOR THE VIDEO!!! Also if my teacher teaches us something like that...i wouldnt understand anything...your video helps alot!

[@brianmclogan]

I am so sorry to hear about your troubles. Do not let your teacher or you define your learning. Keep working hard and let me know if there is anything else I can do to assist you with your math.

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Epic, modern hero amongst students.

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Wish I had you in high school! Great job!

[@brianmclogan]

Jimmy Kelley thank you happy to help you out

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Good teaching method sir

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118 videos on ellipses? Now that's epic.

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This guy teaches pretty well! thank you so much!!

[@brianmclogan]

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

[@Riflez308]

4 years later still better then our Pre Calculus Teacher

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THIS TUTORIAL EASED MY ANXIETY THANK YOU I LOVE YOU

[@brianmclogan]

you are very welcome!

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Thank you very much for being utterly clear with your explainations to students questions. The fact that it must be a trinaomaol square is so important to getting a b and c!

[@brianmclogan]

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

[@aashnachand4675]

I'm ready to ace my test tomorrow, after not knowing what I was doing up until now! Thanks!!!

[@brianmclogan]

best of luck!

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I have viewed 4 other videos at the expense of about 21/2 hours. Whew, you blew them all away. Thank you Sir. University of Houston Downtown.

[@brianmclogan]

Thomas Ratliff Alright! so happy to be able to have helped you out!

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I don't know what I would have done this quarter without your channel. Seriously, I've gotten A's on all my midterms because of your help. My final is in a few hours and hopefully I'll get an A on that too. Thank you so much!

[@brianmclogan]

so happy to help you out! keep up the hard work and best of luck on your exam, let me know how you do

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Thank you very much, i'm taking my precal class online and i have a hard time understanding from the book but these videos help a lot.

[@brianmclogan]

medumdum awesome! happy to be able to help you out

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i wish all teacher teaches like you,

[@brianmclogan]

happy to be able to help you Geomarie!

[@alexandraarmstrong999]

where did you get the (1,-6)?? btw, you're a good teacher I'm understanding 1 month of math in your minutes of videos

[@brianmclogan]

that is one of the vertices. It is a distance 4 which is a from the center

[@carlosguzman2925]

I have my final in a few hours! Thank goodness for your videos. I literally been understanding things so clearly!

[@brianmclogan]

happy to be there for you Carlos! best of luck!

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Thank you so much! This really helps. I'm in 11th grade right now and we have pre-calculus, so I'm trying to study in advance 😁

[@kallabotz5253]

Wish I had you as my professor.

[@brianmclogan]

still making videos every day, let me know if there is anything else I can do to help

[@kidusfikadu1060]

Thank you ,your videos are always helpful

[@brianmclogan]

You are very welcome!!

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your videos are such a huge help to me. thank you so much!

[@rahulsah3082]

Thank you, sir. This video covers a good concept.

[@jbuno9756]

Thank you very much, this is our topic, thanks a lot and I learned a lot.

[@jordangallagher215]

2:10 Tompleting the Tuare! hahaha I love you brian! Just got a good chuckle while studying for my final.

[@keenanweind1780]

It may be useful to consider the minor vertices (the x-axis in this situation): (3,-2);(-1,-2)

[@Squamington]

For (y+2)^2 what did you take the square root of in (y^2+4y+4) to get that 2 in the parenthesis? You were done doing this part of the problem at 5:58

[@ryanpage7272]

Doing work in Calculus II and this helped me out a ton! Thank you!

[@brianmclogan]

awesome! happy to help

[@riverarenserkeitlyt.1227]

Mister what if what I am going to do is transform the standard eq. To general eq.?

[@dovydassernas9191]

Big Brain Brian, I thank you very much

[@matthewmccool7439]

thank you so much! i missed the lecture over this and have spend 2 hours in my math lab trying to understand this.

[@brianmclogan]

+Matthew McCool happy to be able to help out!