Equation for parabola from focus and directrix | Conic sections | Algebra II | Khan Academy

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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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[@lee_voug8357]

Because of this parabola I lost my childhood and teenage days

[@saedcruzreyes5092]

WHY? xD

[@DarthCrustyYT]

@@saedcruzreyes5092 the first video in this series was uploaded 12 years ago to the day I’m writing this and this video came out 6 years later

[@ryannmunoz7136]

Everytime I struggle with my algebra, I come here. I do online school so it's hard to move forward when I'm stuck without my teacher getting back to me (especially since I'm a night owl. I normally have to wait until the following day). Thank you! I'm bad with numbers but when I watch these videos they (sort of) make sense.

[@srutishaw6115]

Ryann Elizabeth Same here. But i m not a online student.

[@dhruvkhandelwal.]

5:21 **Right side of the screen exists** Sal: it's free real estate

[@Brandon-xm4mp]

thats when you know that sal loves realestate

[@zionj104]

Dang it, you beat me to it

[@kellacanb]

"Hairy algebra" he says.

[@TheHiddenChronicle-b9l]

I like my problems nice and hairy

[@NoahCartee]

when your teacher gives you a question on a test that he has never covered...

[@florencecuomo]

"hairy algebra" can we just

[@ryanio123]

Really fantastic Sal. Thank you so much.

[@nikhilverma4976]

Thank you! I was in need of such a video for computing voronoi diagrams in my project

[@amazingunseen681]

Thanks Salman khan to create this Educational Organization!

[@alextrezvy6889]

The link under (Missed the previous lesson?) is broken.

[@GiuseppeLospalluto]

Thank you so much man ! You are fantastic

[@yomahadar]

Which software do you use to write everything?

[@padme8013]

for what grade is this mainly on? like 8th, 9th, 10th etc.

[@saedcruzreyes5092]

11th I believe

[@shreyashprakash879]

@@saedcruzreyes5092 bruh i am in 8th grade

[@charmendro]

5:20 "Let me give myself a little bit real estate over here" lol

[@lucyheartfilia4607]

How do I find the equation of the ellipse given only that the the major axis is vertical and the graph passes through the vertex of a parabola?

[@甘木-m5r]

Define childhood ..... do I remember parabolas from my childhood? ✨📚🍨🍉

[@jimbernabe2289]

I watched another video regarding this. It demonstrated another formula (y-k)^2=4p(x-h) Is this formula applicable?

[@abdullahraja5357]

I think that's the case 3 and 4

[@jeffthevomitguy1178]

Yes the difference is the formula he is showing gives the parabola for all possible quadrants. (Y-k)^2=4p(x-h) is used only on horizontal Parabolas and you can reverse it with (x-h)^2=4p(y-k) for vertical ones.

[@kevinpena2741]

does anyone have answers to a sheet where we have to solve questions and its called the Focus and Directrix of a Parabola and its a leprechaun drawing on the back

[@fjkldhakljf]

Thanks I will just memorize it

[@MrDands]

Fascinating indeed

[@patrikchristian2071]

what if the equation of dirctrix includes 'x' also?

[@MuDasirYasen]

In that case the principle axis of the parabola will lie at some angle to the x axis and perpendicular to the directrix.

[@azrielsshadowsinger]

my brain can’t handle this- what did he just do

[@sarahmotherway3410]

" Hairy algebra" *Shivers*

[@kristophercloud2567]

How do we find the focus or the directrix when the vertex is (4,0) and solving for y=? I can’t find anywhere that answers this. My question is to find if there is a minimum or maximum of the equation y=(x+4)squared.

[@jeffthevomitguy1178]

There is a min of 0 and max is ♾

[@FasAntick]

how can we find the equation of a hyperbola given the focus and directrix

[@highlights9175]

commenting on 6year old comment sir how's life going?

[@rdscombatpro5650]

Thank you !!!

[@tutstorial8474]

isn't that supposed to be a - x ?

[@thebiggestobjfan3344]

tnx alot !!!!!!!!!!

[@tungeshnaidu4569]

Shouldn't it be (a-x)2+(b-y)2 instead of (x-a)2+(y-b)2

[@ayushi6703]

In both cases answer will be same as it contains square .

[@tungeshnaidu4569]

yes, thank you.

[@aftabali9372]

the point in last was the coordinate (x,y) or (a,b)

[@ayushi6703]

If you ask about focus (1,2) then it is (a,b)

[@big-pp8582]

Take a shot for every “hairy algebra” 😂

[@rishijarral4320]

love yall

[@kellacanb]

That formula applies to ALL parabolas?

[@JM-lh8rl]

Kella Boiarddi Yes

[@jhukelx]

crying and laughing at the same time. lol "hairy algebra" it is!

[@brittknee3884]

I’m a little stupid so I’d like to know how you got “-2yk”

[@ayushi6703]

As you can see (y-k)^2 =y^2+k^2-2yk , it's just a simple expanding formula

[@vusumuzitembe9647]

tnx

[@anirudhsoni722]

hey thanks !!

[@BeanSprouts02]

1:29 What’s the purpose of using the distant formula here?

[@BeanSprouts02]

2:08 And what do you mean negative? The final answer will be negative or will the y variable be the negative variable instead of the x variable?

[@yashsingh963]

nice

[@danielbugtong6795]

y-k then y=k so it means its 0?

[@MuhammadBilal-hm4gy]

what if directrix is x = a

[@alexmisra6690]

This makes no sense

[@ayushi6703]

Why ?? 😂

[@smath82]

The directrix cannot be y=k since k is the why coordinate of the vertex >_

[@Gabriel-nf5zt]

hola que tal, como les va

[@yourroyalhighness6297]

"It looks really hairy." HAHAHA

[@joshua8704]

THE PAIN!!

[@jarodtunacao6241]

lumilipad nanaman ang isip ko

[@experimentoruser9917]

i dare you to prove parabola opens left

[@isabellacuadras4373]

Hate math!!!!

[@fredward2428]

Sus 😳😳

[@mrspumpkin6756]

not helpful