Foci of an ellipse | Conic sections | Algebra II | Khan Academy

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Calculating the foci (or focuses) of an Ellipse.
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[@blakeobeans]

btw, this is the law of planetary motion that Kepler used to prove that the earth revolved around the sun.

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A fancy way of telling spin is preserved

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Wow 12 years comment

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balls

[@user-fq6yl3sn3y]

I translated this video in Korean :) 제가 번역했어요 :)

[@tommyl5319]

I'm here literally because I remember the words focus/foci and that they were special points along the major axis of an ellipse from high school, but I couldn't remember what the significance was. I kind of want to try implementing this in a program to do something fancy now

[@DarkAlpha171]

how do you find the coordinates of an ellipses focus when you don't know any information about the equation.

[@vivianvillasenor8373]

It finally makes sense! Thank you :)

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I have a crush on math. Thank you Khan academy😊😊😊.

[@pastariceboy]

thank you so much i was sick from school, and i bet this is better than what i would have learned!

[@prim16]

Thank you so fucking much I couldn't understand foci... ._.

[@moj543]

thank you so much.... i finally understand ellipses now!

[@1dinanov]

That was great. Thank you!

[@medievalmusiclover]

Another great explanation! Excellent.

[@SASUKEUCHIHA-yc6er]

Thank u so much ....

[@aniruddhvasishta8334]

I see a lot of comments asking what if the ellipse is tall and skinny (or if a and b are switched). It's really the same thing if you think about it; it's just a 90-degree rotation of the one shown in the video. I think a and b would just be switched in the formulas (I'm not sure though).

[@ShenoyKitchen]

thx..... very happy with this

[@Lavabug]

Nice, it would be cool if you discussed on Kepler's laws of planetary motion with this!

[@sophaura]

So helpful!

[@alkalinedogie]

THANK YOU SO MUCH!!!!! Very helpful thanks man.

[@IrfanMirK]

thanks a lot salman sir......u made things so easy for me.....thanks once again

[@Sylvanas17]

THANK YOU!!!!!!!!!! UR AWESOME!!!

[@raxtar107]

thanks.. this really helps!!!!!!!

[@GenericCoder]

Really interesting video thanks alot great explanations.

[@dchangebegins]

Thanks as always...if u could pls do a video on conjugate diameter of ellipse. It will b big help.

[@thomasevers1938]

very helpfull for my investigation

[@kshitijchauhan1479]

U are a really great techer

[@Benjikj]

can you do a video on the proof of the foca/optical property!!

[@toriatong]

OMG thanks u sooooo much!!! u r a genius!!!

[@Dharmendar.Kumar2023]

Loved it.

[@NirmalKumar-nd4ll]

You r great sir, 🙏🙏🙏

[@MASTURCHEEF001]

well, if you have the co-vertices you know the minor axis, because they are the shortest points from the center of the ellipse. with the focus you can work backwards to find the major axis. With that you can derive the standard equation, given you know where the origin is.

[@Benjikj]

can you do a video on the proof of the Focal/Optical Property for ellipses, thanks

[@codemathlab]

This is Amazing. The best KZbin channel on earth.

[@Xx0Mystic0xX]

Thx alot! BTW Is a vertical shaped ellipse different? How would you find the coordinates of the foci of that?

[@dariawicgs5254]

isn't the last scene's left focus'coordinate should be（-1-√5,-2）???if I'm wrong,please correct me...

[@twinnerlarry]

Daria wicgs No. You are subtracting sqrt5 from the origin. The origin is at 1

[@dariawicgs5254]

isn't the last scene's left focus'coordinate be（-1-√5,-2）???if I'm wrong,please correct me...

[@manavaggarwal3944]

very nice video and content has been explainrd very beautifully

[@nikolakerleta3084]

How can we prove that the sum of the distances from any point to the foci stay constant?

[@arshisid47]

Wonderulllll.

[@classiclife93]

You are amaaaaaaaaaazing .. Thanks SoOoOo much That was very helpful .. Keep going ;)

[@Gearmasher1]

you may have just saved me from failing my test on monday! Thank you so much!

[@smf5769]

how did it go

[@Spellbook]

@@smf5769 dude its been 10 years haha. he/she probably passed by now.

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Nah idts, they're not responding cos they failed

[@katestohl2273]

i want an update

[@Gearmasher1]

Wasn't expecting to see this on a 10 year old post BUT I passed, went to college, and got a good job. This video definitely helped.

[@Ditiro100]

Question If the major axis was parallel with the y-axis where going to add and subtract the y-value?

[@deewahhht]

Thanks. My final Extension maths exam is in 3 days and this helped heaps!

[@deewahhht]

Ryan Park yes I passed 8 years ago 😂

[@theaceplaysxd]

what software is he using to draw this stuff?

[@wasabiclown]

Hey Marvin's Analytic Geometry Class!

[@Bryan2394]

Thanks

[@johnpatrickalconescorpuz3111]

Ty

[@magnusjensson8199]

Hihi, great thanks. I have a question: Can I find a Foci if I only have major axis and one point on the ellipse.

[@laurencrom]

Hi Kentaro!

[@mathhouse798]

An ellipsis goes to circle when ditanance between focies goes to zero

[@chotramnauthprabhu7538]

Thank uuuuuu

[@skyrex98]

I HEARD A DOG IN THE BACK GROUND O.O at 8:12

[@yoitsmei3615]

wow... almost 10 years ago now

[@joshlete]

Is "a" always the semi major radius, for example if you switch the denominators 9 and 4(vertical ellipse), would "a" still be 3 or would it be 2?

[@drzokoenfacebookpage8626]

Good

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i think you can give a donation to the academy ;)

[@zhevsky17]

this video saved my math quiz score :))

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The spider in your avatar is the first little gag like that I've fell for in a while

[@midori58]

Now this is where I get confused. So when you say that F1 + F2 = 2A, do you actually mean F1 + F2 = major diameter? Because things gets messy when the ellipse stands upright (B > A). Because in that case, the variable "A" in the equation is representative of the minor radius, but does the equation F1 + F2 = 2A still stand? Or do you actually mean F1 + F2 = major diameter and things just got confusing because we keep using the same variables.

[@ThomasGiles]

In the example, a is actually 3, and b is actually 2. Right? Also, would be nice to prove f=2a, as someone else has suggested.

[@theprocessionist6442]

These videos have been helpful to me, as I'm developing my string theory. :D

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scientists are dealing with mathematics that aren't even taught in school, or on youtube videos (the cutting edge), that deal with string theory, i doubt u'd develop it. Plus there already is a current theory for string theory that TON's of mathematicians and scientists worked on. And if that doesn't cut it, it's most likely something we didn't discover yet that's stopping it. But knock yourself out.

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Why say that before looking into it?

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The Processionist wow, i just told you. But knock yourself out, not trying to stop you, i was just informing you in case you weren't already.

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No harm done. You might take a look at my model and find me on facebook. Start fresh and check it out. :D

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@@theprocessionist6442 have you solved it yet?

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so pumped for the math test tomorrow!

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was it useful after 7 years?

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@@kimothefungenuis yea time flies

[@Matt-vh4pr]

Khan Academy is much better than my school

[@lphuff]

I'm a teacher and I am very interested in what program you are using to make this video. I thank you in advance.

[@MrLolza69]

Tons of subscribers+views= MONEY and also the self-satisfaction he gets from the encouragement of his many viewers :)

[@qwertyuiopasdfhjk100]

What about ellipses that have a y orientation? When b is greater than a. Do we still use f equals the square root of a^2 - b^2???

[@roguefox4308]

+Edward Sim Hope this isn't too late being 5 months ago haha. But you would then switch A and B since your Triangle is not in a different orientation.

[@MuDasirYasen]

Caleb Marcum 👍

[@rajyalakshimi411]

What if they give me the co-vertices and the foci and ask to write the standard equation?

[@abdouamaadour5451]

But why does d1 + d2 = constant at the first place ?

[@chintu844]

abdou amaadour its a property of ellipse. just like radius of circle is always constant for every point on the circle

[@nabeeghahmed8530]

Why are you what you are?

[@abhayshankar8762]

Definition of ellipse.

[@yeowool3358]

And then everything clicks…

[@jackgogvail2565]

Yeo Wool don't you just love that

[@ahmadzaka9885]

I swear. I've got a major exam in 7 days and I've been trying to get my head around conics for the last 3 days and now I watch this and it all seems so easy.

[@andyverajr2170]

why is the center (1,-2) ?????

[@ItsNeuroscience]

I don't understand, why do you have to say "(one plus the square root of 5, -2)"? When finding the vertices(of the major axis), shouldn't you just be able to count, in this case, plus or minus two along the x-axis from the center of the ellipse? Thus, making the vertices of this ellipse (3, -2) & (-1, -2)? Why the square root of 5? Why add the foci if it just represents a point of focus for each parabola???

[@lkrauss100]

I think you're wrong when you say a>b means that it's horizontal. it's horizontal if the x value is over the a value, and not the y value

[@abhijitroy3854]

Why ellipse has two focus?

[@Xavier-fk7wm]

You should post an example with meters not invisible numbers it difficult to understand.

[@danielmcmullan1001]

Don't lose focuses!

[@kamlakarchaudhari9800]

It's good but I can't understand the concept of foci

[@rupalibatta3075]

At 5:57 he says the minor radius is a. Isn't a the major radius?

[@sagniksaha7359]

Rupali yep

[@VirgoINFP]

Are the foci always symmetrical?

[@MajSigmaE]

Sally Chan compared to the center, yes.

[@maddiexmcg]

honestly how many more times can you say d1 + d2 = 2a

[@ClintonFD]

wow

[@knowledgepower7286]

wow

[@tmateek]

Schrodinger's Doge wow

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Ahmad Alzhrani wow!

[@DragonRazor9283]

wow

[@cloudyt6600]

Wow!

[@kemalyanmaz3080]

İn 13.05 √5 is equal to 2.23 and focus (3.23,-2) but this point is not in the elips

[@abhisheaksharma3765]

Ia focus doesn't have to be on the ellipse

[@821marko]

A thought that occurred to me was that the foci specific to an ellipse are actually the radius of the circle that would be formed were that ellipse shrunk back to a circle...the circumference of an ellipse were it re-formed back to a circle would have the same circumference as the ellipse and one of those foci is telling you the radius of the circle specific to that ellipse...I suppose this is well covered ground in more advanced properties of ellipses, but I have been out of school for so long seeing your videos has helped greatly in many subjects like biology and physics etc......again I thanks and happy New Year !

[@anilkumarsharma8901]

show graph of everything in ellipse so we find out actual position of foci ???

[@wasibeg6205]

I am here in sep 2021

[@kuulgangster]

This video doesn't quite explain how the equation F1 + F2 = 2a. Could anyone help me with that?

[@umaerabdullah1036]

what's the proof of d1 + d2 = 2a.. please explain

[@Nobody-Nowhere-Nothing]

He made a video about it, check the conic sections playlist

[@wohoomaster9068]

Could you please tell us the title? Or pass a link?

[@LukeSumIpsePatremTe]

It's in this very same video kzbin.info/www/bejne/h4OVp6ucrM57d7c From the definition of an ellipse: the sum of distances from focii (focuses) is a *constant.* Then we pick a point from an ellipse, that is also on a major axis. Hence the sum of distances from foci, is the length of a major axis. And since *a* is half of major axis, the distance is *2a.* Since the sum of distances from foci to any point on ellipse is a constant, and we know that distance in on special case (when we pick a point that's on a major axis), then we know that what ever d1 and d2 are, the sum d1 + d2 = 2a.

[@lucasmez]

lol...back when youtube used the stars

[@jhonma1]

Thanks for the explanation

[@ompmega]

My teacher sent me here

[@k1tozen668]

no sound

[@drettlinking]

G+H is the same as G+H

[@angcientrock]

yeah you should >:(((( jkjkjkjk

[@MrDevilboy1996]

the 7 people who disliked this are teachers that don't know how to teach :D

[@rajeshraut2955]

Is f is half of a

[@ReenasCookeryBook]

This comment section is as old as time.

[@Soumyayoutube]

How is d1+d2=2a?

[@deathball2331]

Soumya Negi the mathematical property of an ellipse is that the sum of d1 and d2 will always equal the major axis, and since a is half of the major axis, the distance will be 2a

[@Soumyayoutube]

@@deathball2331 thanku 😀

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teachers

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[@TheSpyker123]

Sal what do you get out of this? I mean superman gets lois lane batman gets a cool car what do you get for saving millions of children's futures

[@roarhorn2520]

how can you get the value of "d" instead of not knowing any information about focus? IS there any defined structure for this? I am too much confused rather than being helped.