Proof: Hyperbola foci | Conic sections | Algebra II | Khan Academy

[@gyararay]

if u made it to the end, thumbs up

[@numbersletters2920]

1➗1➗2= 0.5 ➗3=

[@lexinaut]

You come 2a helpful conclusion in an elegant manner. The video provides focus and clarity regarding the foci of ellipses and hyperbolas. Should this one be called a Conic Cademy Video?

[@parahumour4619]

Lmaooo, I'm dissapointed no one appreciated your pun in 11 years

[@lexinaut]

@@parahumour4619 Thanks! Sometimes these puns are “delayed action.” 11 years, though🤣! That’s really something!

[@nocturnalvisionmusic]

@@lexinaut you're still on KZbin wow :o hope you are doing good! :D

[@marcryan658]

Holy crap. I can't believe this made sense. I was convinced halfway through that I wouldn't understand anything.

[@universe378]

This is great. Great to see proofs like that. Its good to see the logic. Looooove your videos. Working through them all!

[@lexinaut]

GREAT JOB with a very tiring but important proof involving lots of finicky algebra. There is one little notation error involving a misplaced exponent near the end, but anyone who has gotten that far will not only probably forgive but understand the glitch. It didn't affect the answer because you continued as if the mistake wasn't made.

[@lexinaut]

You’ve really put the FOCUS on the FOCUS and the LOCUS here! Thanks!

[@nocturnalvisionmusic]

12 years later but gave this awesome pun its deserved like :)

[@jsgandora]

Thank you so much for this video! I couldn't find this proof anywhere, and you gave it just before my conics test. Thank you so much! :)

[@сушкаотходов]

Thanks from Turkey

[@sdhafele5003]

7:28 Did anyone else hear Sal's phone ring? LOL!

[@contentresults]

@ 13:46 my mind melts away

[@lazmedina]

I gotta give it to you, I almost understood what I was never meant to understand in the first place. Thanks!

[@YZhou-g5q]

"See my phone is ringing, let me turn if off." lol

[@谭佳-o6c]

这个推算太强大了！必须点赞❤

[@FutureAstronaut_Ganesh]

This derivation is too great ,while our class teacher just gave us the formula and told us to solve formula based questions Thank you sir I was really curious about where the formula derived

[@firstfrost1234]

that's so amazing you are a genius thank you so much for your wonderful lesson ^^ i love all of your videos so much you are the best teacher !!!!!!!!!

[@IGIMYM]

Haha woooow! Awesome! I have never enjoyed math this much! Thank you so much!

[@Kueen24]

Thanks for the video 👏👌

[@chefethanguo9701]

Biggest literal equation right here.

[@danialdunson]

I am satisfied Khan Acadamy

[@Dozellzen]

no phones in class lol. your videos are a big help

[@ThaMC22]

thank you for this video you are a life-saver!!!

[@georger.9020]

Would someone mind explaining 5:30-6:30 for me please, I just didn't understand how he got 4a^2 + "4a" sqr rt ((x-f)^2 + y^2) + "(x-f)^2 + y^2" Used quotes to point out which part confused me.

[@georger.9020]

oh shit, never mind lmao figured out after like 30 minutes of wanting to shoot myself in the brain

[@georger.9020]

If anyone had issues like I did recognize what he did here: (2a+ √((x-f)^2 + y^2)) x (2a+ √((x-f)^2 + y^2)), which gives you the answer: 4a^2 + 4a √((x-f)^2 + y^2) + (x-f)^2 + y^2

[@sparrdog]

same issue here , thanks for pointing that out.

[@ngc-ho1xd]

Sal wasn't kidding, that was Hairy!

[@Petelecaster]

wow that blew my mind

[@speedmusic8067]

Im sorry but I got confused by 12:30 . Can someone explain that part to me? or what I need to learn first before I can comprehend that part. Thanks.

[@bukpuki]

There Sal has a fraction (f^2/a^2 - 1) / (f^2 - a^2) Then he just multiplies both numerator and denominator by a^2

[@linyixiu3122]

SpeedMusic There was a mistake in his working. The ^2 should be inside the bracket with the a to give a^2 (f^2 - a^2) instead of outside the bracket.

[@yuskei3]

He could have done that, but he decided to divide by a^2 later, which gives the exact same result.

[@Shkencetari]

At 12:15 don't say that they cancel out, because if we cancel (remains 0) so the whole expression would be 0, but instead of that just say we simplify this by that.

[@elementoxygen]

Didn't you say on your last video that |d1-d2|=2a Anyway, Great video!

[@fornillosjohnoliver2193]

👌👌👌

[@chessvid7600]

How did you factored out thex^2 in ×^2f^2/a^2-x^2-y^2=f^2-a^2?

[@LoneAssassinX]

WoW!!! just one Q. at 8:44 why did'nt you divide by 4a?

[@neosud2064]

It would have been even messier to do that

[@MartinKrauskopf]

@huashife He can't. There was a typo/error in previous step. Where in denominator should be a^2(f^2-a^2) instead of a^2((f^2-a)^2). Then you can cancel out (f^2-a^2)/(a^2*(f^2-a^2)) to a^2.

[@juroxy14]

how do you determine the principal axis of a hyperbola? plz help

[@erickjoshuanebreja6154]

juroxy14 what do you mean principal axis???

[@JohnDixon]

It's the axis in the direction it opens

[@TheMick26]

You're very strong mathematically! Thanks for all the tutorials! BTW, why didn't you answer my call? ;o)

[@jmm00702]

lol@ ur phone. ur really helping me here, been some hours on your vids and seemingly ill be more. if i pass my exam 2morrow ill save my career progression, and i will fucking love you, no homo. xD

[@charljustinereyno1418]

How do i know that the opening of the hyperbola opens upward or downward or left or right

[@xiaoyuivy]

if the sign of the y is positive then it opens up and vice versa

[@jasonli1060]

Quite nice, but I have my misgivings with the end of the proof. How would one, not given the original equation of a hyperbola, derive the formula b^2 = f^2 - a^2 ?

[@MartinKrauskopf]

@mikepuc1 I have to disagree. If I follow video from the beginning to the end I do not have any problem with writings (never even though about problem in writing, until I saw your comment) since I have Sal speaking on the background. If I would jump into the centre of the video, might be.... Just opposite experience after watching my 157th Khan Academy video :). Otherwise nothing against constructive critics - that's on place.

[@david-yt4oo]

why does everyone just assume that "f squared minus a squared is equal to b squared"? can someone actually prove this please?. I'd like to know what the actual relation of that somewhat-pythagorean equation means. maybe there's a right triangle involved in this? (there should be one)

[@dhiwakark]

daniel He didn't assumed that..He proved that...See the final equation...

[@JustTruth-x7g]

bro why are there beeb sound

[@cinquain0]

I can die in peace now

[@akam9919]

Anyone hear a beeping sound?

[@Jakers2009]

Sal... why is maths so much easier and more interesting than finance... but they pay you more for finance...

[@nathanielpekas950]

wow

[@iNowHateAtSigns]

Math like a boss...