Conic sections: Intro to ellipse | Conic sections | Algebra II | Khan Academy

[@liammccarthy9388]

Khan academy is honestly better than my teachers at school. Spent an entire unit not understanding this stuff and now i completely understand it within like 10 minutes

[@josephmiranda1246]

I know exactly what you mean

[@zachf.7854]

this guy is better than my professor; I've learned more in one video than the week we spent on this stuff

[@brynechibaya3407]

way better than mine too

[@jaynimje3790]

ya it's true

[@tau6582]

lmao ikr

[@stinkyradish6935]

Facts

[@madfrog9213]

you are right

[@andrewg.5011]

You are amazing man. You are literally saving my life right now in math. My prof is terrible and I've learned more from 3 of your videos than I've learned my whole semester! Thank you for existing and making these videos lol

[@iamyourfan7381]

I KNOW RIGHT!!! HAHHAHA

[@AezazAZYAli]

One correction: a will always be the length of the semi major axis. If the ellipse is "short and fat", a would be along the x-axis. If it is "tall and skinny", a would be along y-axis. By convention, a is never shorter than b.

[@bonzai8584]

Aezaz Ali that's why it's x^2/a^2 + y^2/b^2 because a is along the x axis and b is along the y axis. If a is greater than your b then it is called the 'major' axis, if b is greater than a then a would technically be called the minor axis because the length of a to the center is shorter compared to the length of b to the center. The minor axis and major axis can be used interchangeably depending on the value of a and b.

[@ahmedihsan5254]

@@bonzai8584 my teacher told me that if the length in y is greater than it is in x, then it should be x^2/b + y^2/a because a should always have a greater value than b but i think its just like you said, they can be used interchangeably, its better and more practical this way.

[@susantparida8369]

A and b are just variables, use them as you wish.

[@nikitadubrovskyi4050]

Susant Parida this isn’t open to interpretation, you can’t just “use them as you wish”

[@OrganicChemistryDoc]

@AezazAZYAli youre right

[@subscribingtoeveryonewhosu4927]

Sal you are AMAZING you have really changed my life! I went from just getting my in my math class in 6th grade to trying to skip two grades this summer so I can study precalc...all in two years!

[@badymojoy]

I definitely got a lot out of this video. Thank you Sal.

[@juenarosecleofe9183]

Conic sections used to be the cause of my panic attacks back in 10th grade and also ebcaus eof the teacher that made me feel anxious during the lesson. Khan Academy is such a life saver!

[@carmalae]

In 14mins, I finally understood what my professor was trying to discuss for almost 2 hours. Mr. Khan, how I wish I had you as my professor. I'd surely understand every lesson well if you are. Thumbs up for this vid! Thank you so much! :D

[@chineee123]

I take algebra II online, and when i dont get what they teach(which is most of the time), the teachers themselves recommend you! You've actually been teaching me!

[@appealingbanana7463]

Love how you don’t just give out the formulas for people to memorise them, that takes all the fun out of maths, thanks for the intuition cues

[@lomekii]

"So let's say I were to show up at your door...."

[@numbersletters2920]

Well eternally grateful.1➗A=

[@BigiantB]

Sal you are the man.Hands down.May you always have a spot light on the tube.And may people throw rose peddles at your feet.

[@jonathanmiller2913]

The guy is super helpful but every 90 sec or so he swallows and it sends nasty chills down my spine

[@9loveylove]

Thank you so so so so much! I have a huge test tomorrow, and all of your videos are helping me understand all of the lessons my teacher doesn't explain well!

[@lexinaut]

LOVELY VIDEO. It took Kepler EIGHT YEARS of meticulous calculations to prove that Mars moved in an ellipse. He had to throw out the perfect circle which religious dogma insisted must be the shape of orbits. Respectfully if humorously, I propose that KEPPLE be given the meaning "to calculate precisely and CHECK YOUR WORK!" Kepler wrote his own epitaph (in part): "Mensus eram coelos, nunc terrae metior umbras . . ." I measured the heavens, now I measure the shadows. KEPPLE away!

[@verbotencloud17]

i have a test that i’m taking in an hour and a half and i’m just now learning this

[@austinchun5809]

Once again, Mr. Sal, you always amaze me with your incredible teaching ability. Thank you so much.

[@cherrycandelabra309]

Dude ur awesome

[@dragovragovich4249]

+cherrycandelabra ure*

[@Monkeymaster1106]

Thanks, i finally found a good tutorial =)

[@321Sequence]

without these videos i would have failed Conice. Thank you Sal!

[@dannespringles2687]

there are reasons for why you can't fully understand certain topics in class. no. 1 reason = Distractions, talking to classmates a lot. that crush you keep looking at, and actually forgetting to pull your earphones out.

[@surfinshredder]

Every time I watch Khan's videos this is me ----> (>0.0)> Mind = Blown ... "Why don't my professors explain it that way?"

[@snoozes]

I'm learning about ellipses in math right now and your video really cleared things up for me. Just a small tip though: a always has to be the largest number on the bottom. So in your sample problem a=5 and y=3, not the other way around. That's how you tell whether it's a horizontal or vertical ellipse from looking at the equation. If the bigger number is under y, it's vertical :)

[@iMusikkForeva]

I noticed the same thing!

[@RussianAsian8D2]

10th or 11th. This was one of the last things we learned. I took an adavanced so I was able to learn this sophomore year which ended this year :D

[@jmath6589]

The attack of the colored lines!!!

[@revanthnani9427]

Khan academy helped me to cover all my delayed syllabus . Thank u so much

[@Gottasuckit]

Extremely well explained I already understood the concept but never heard the word semi-minor axis thank you for educating me :)

[@CliveReyes]

@clevercleverchris In the ellipse that its center is the origin point, The point (0,0) is not a part of the curve.. u cant get both x=0 and y=0 at the same time.. But when x=0, y will be equal to b, and when y=0 x will be equal to a. So yes the point (0,0) does not satisfy the relationship because this point is not included in the curve..

[@Name-yu6ux]

Tysm best video in youtube currently❤🎉 EVEN AFTER 15 FREAKING YEARS

[@tb2748]

So how is the formula for the ellipse derived? Is it also an application of the distance formula/pythagorean theorem?

[@C4bombpro]

You're everything my math teacher isn't.

[@iamyourfan7381]

Thank you so much for this...

[@LilTom895]

this is good for when absent from algebra class

[@jennipacheco7924]

SUPER EASY and I’m self teaching ! :)

[@cheponchocho2]

i think it would be easier for the students to learn the complete formula (x-h)^2 /a^2 + (y-k)^2 /b^2 = 1 explaining that (h,k) are the coordinates of the center of the ellipse, i.e. if it's centered at the origin (h,k) would be (0,0). That way you could graph an ellipse anywhere on the plain without having to do much more thinking.

[@jwelke1987]

Love your videos. "a" will switch places with "b" and end up under the y^2 sometimes though. "a" is always the larger term.. not certain it matters but I've seen a breakdown proof where "a^2 - b^2 = c^2".

[@lkrauss100]

I wish we used these videos in my actual math class

[@samanthak.2706]

Thank you so much Sal Khan!!

[@mnbvcxz995]

any videos that explain eccentricity?

[@tjtigley8693]

sorry if it was in the video and i missed it, in a bit of a rush. Given x^2/a^2 + y^2/b^2 as position 1, and x^2/b^2 + y^2/a^2 as position 2, how do you diffrientiate the two and determine whether the ellipse is in position 1 or 2 when values are in place of "a" and "b"? Thank you in advance

[@hitenderrana7268]

It's really helpful 😊😊

[@TK-xi1jb]

Excellent, on point explanations.

[@nicoleedee1]

thanks that was really helpful. just wondering how to show the S'P + PS = 2a?

[@marioomaehab]

thank you very much it was such an accommodating lesson that has extremely helped me i have really understood it thank you once again

[@Prasad-eo8se]

good

[@sheena_e]

Do you have a video for the derivation of its equation?

[@GenericCoder]

Thanks a lot your explanations are really perfect.

[@12thando34]

thankx for all your vids hey...thunk ima finally get somr good marks for my algebra

[@Peter_1986]

Well, to be fair it is slightly easier for a teacher to make sense in instructional videos - a school teacher often has to work under pressure in order to cover a whole chapter or something during, for example, a seminar. But of course, a teacher should always try to explain the core of everything, and exactly WHY it works a certain way.

[@hubsterrecords1521]

This helps so much as an 8th grader doing this right now in A2, wish I could have used this at the start of the marking period.

[@hanumanaska292]

HubsterRecords, I'm a 6th grader doing this!

[@nessy3098]

hanumanas ka I’m a 3rs grader doing this!!

[@Jakers2009]

The general function is x^2/a^2+y^2/b^2=1

[@chufengxilin9869]

That derivation of formula help me,thanks

[@julianzhuang9552]

I love Khan Academy.

[@JohannesNamutuwa]

No school for the next six months because of the Corona virus so I'm here to study in advance. Thank you so much sir.💎

[@blahblahbluebird]

THANK YOU i have an algebra 2 benchmark test tomorrow and my teacher was unclear about conic sections

[@leedavid2396]

Can you do one on making equation shortcuts

[@bushpilot223]

@TermLee No because the larger number us under the X so it would be fatter. If the larger number were under the Y it would make it taller. It doesn't matter which side it is on, it matters which variable it is under.

[@bushpilot223]

Is there a video that will help me with simplifying into standard form? Like if I wanted to find the standard form of 9x^2 - y^2 - 36x - 6y + 18 = 0. How do I convert that into the y^2 over a^2 + x^2 over b^2 form?

[@TanksPokemon]

Thank you so much!

[@OkashaSH5]

Khan!!!!!!!

[@mai-gb2lf]

not @ me sobbing while watching bc i don't get why corona showed up and ruined my ability to understand math thank u khan acad 🥺

[@92potential]

you are going to heaven I can guarantee you that

[@hitenderrana7268]

What about you

[@DannyVarughese]

he's using Microsoft Paint, a program we all have defaulted on windows computers. It's just that he uses it so well that we think it's a top-notch program

[@Shkencetari]

A really helpful video.

[@ajaykumarray8925]

Great video ❤ it

[@TheRichjt]

without these videos i honestly would have failed calc 2

[@OmphileMonnapula]

thank you sir

[@BloodudeXD]

For me, this is pre-calculus, which can range from grade ten to twelve.

[@asharayub4636]

thanks man thanks so much!

[@MegaJOEXD]

yes thank you very much

[@jotone6264]

thank u so much

[@irvingc4508]

They shouldnt have teacher teach anymore... they should just have students watch your videos and teachers be there to facilitate.

[@hanumanaska292]

Irving, can't agree more.

[@izreyo8997]

KYRIE IRVING FROM DOWNTON

[@dannespringles2687]

you're basically asking to redo what society has been used to since the dawn if education.

[@SathvickSatish]

irving c that's never gonna happen

[@devonreine7583]

Sathvick Satish that’s what we do at my school we watch videos like this at home and then do a worksheet in class and if we need help we ask the teacher

[@JuanHernandez-ll8cu]

Thanks

[@CelluloidPDS]

This video is so easy to understand as compared to reading lecture notes 😅

[@JohannesNamutuwa]

True😹

[@denniskinoti183]

thankyou

[@Gokul2007-ih1dv]

13:05 now only i can understand

[@EstebanWolf1986]

god bless you

[@DevoteDev]

What software are you using for making videos ?

[@marcorotairo7776]

What app u used in writing? Thanks.

[@abhishekjal1976]

Sir how did you got the value of a and b

[@JohannesNamutuwa]

Square root.

[@rjxxx9301]

GOOD \ LECTURE

[@cyanideneko8795]

Yea, I like that colour too...

[@WinniedaPoohanPiglet]

I wish he could take my tests for me...

[@margebacci1762]

Why X_5 for x radious? If it is plus 5 towards the right the new origin? Please help me to see it clear?

[@sharayu1]

gr8! thnx a lot!

[@ahmadasa287]

❤

[@michaelsharpe5112]

I wish I could explain things as clearly as Sal

[@deepkushagra]

when we shift to right by a, we subtract = x-a // when we shift to the left, we add: x+a................... for y, it was y+a meant shifting up by a and y-a meant shifting down by a. In the equation of ellipse why have we inverted this principle for y but not for x

[@samanthak.2706]

7:17

[@yassaification]

i'm doing this in grade 11 maths c

[@gemakaren]

Can any one explain to me what determines the maximum width and height of the ellipse? I'm trying to complete a free online course and it just jumped right into this topic with virtually no explanation. Thanks!

[@ahmedelkhateeb4906]

2a is the maximums width of an elipse , while 2b is the maximum Hight . but why is that ? as mentioned in the video > a is the radius of an elipse in the x-direction , so the maximum width = 2a , while b is the radius of an elipse in the y direction , so the maximum height = 2 x radius in the y- direction = 2xb

[@izreyo8997]

When finding the value of a in x^2 / 9, how did you know that it has already been squared? Can't it be 81?

[@raghunandan384]

ItzRiordan because it is equated to 1 which means that the net ratio is 1.in which case the numbers written in the denominator are always the squared value

[@عبدالرحمنالحربي-ي6ب6ت]

thanks nice

[@nvjolley]

It's called vertex and co-vertex

[@ckalas]

im doing this in first year engineering

[@electroamtu765]

What happens if the equation isnt equal to 1?

[@TheQueposfan]

I just purchased into the ellipse (intotheellipse) and would like to make it a center for logical philosophical discussions from various viewpoints. My days of mathematics are behind me but I view the ellipse as an interesting model for what I am trying to achieve. I came across this page and I want to compliment you on an incredible presentation.

[@Sylvanas17]

ur too awesome...

[@VndNvwYvvSvv]

2009 "This is going to be a little bit of a fat ellipse" 2012 "This is a plus-sized ellipse but should be treated the same mathematically as a circle" 2019 "All ellipses are equal and equivalent, except those with a minor radius in the y axis, which are literally n@z!s"

[@PotterAmity]

I think the software he's using is Microsoft Paint. :P