What is an Ellipse? | Geometry, Ellipses Definition, Introduction to Ellipses

What is an ellipse? Ellipses are very interesting shapes, and we will be going over the definition of an ellipse and many related terms in today's geometry math lesson!
An ellipse is defined by three things: two points, each called a focus of the ellipse (collectively called the "foci"), and a distance we will call 2a. The importance of this distance is as follows.
With a distance 2a, and two points F_1 and F_2, the ellipse given by this information is the set of all points such that for each point, the sum of its distances from F_1 and F_2 is equal to 2a. So every point on the ellipse has this property that the sum of its distances from the foci is 2a, the exact same number for every point. It's pretty cool! You might notice some similarity to circle in this definition.
Remember that a circle is the set of all points that are a given distance from a given point, called the radius and center respectively. Ellipses are a generalization of circles, which means that circles are special types of ellipses. An ellipse whose foci are the same point is a circle. All of this information is much better explained with visuals, so check out the video lesson!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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[@WrathofMath]

Take a break from studying to check out my math rap channel! kzbin.info/www/bejne/aJrGfYh-g86ies0

[@ahmadshilleh9990]

Can you explain sun position in the ellipse on how and where it got positioned?

[@kadensadich1311]

Bro thank you so much for the video, you described it without sounding monotone and ur channel name is amazing lol.

[@joelstolarski2244]

That was a very nice explanation. Learning 3d design, and some of the tools in Fusion 360 , require knowing geometry. Long time since college geometry. Thank you for making this very understandable tutorial on ellipses!

[@WrathofMath]

Glad to help - thanks for watching and good luck with 3d design!

[@user-ol7gq8bl9t]

I'm so glad I found your video. Thank You for this sir!✨

[@akhan1107]

Thank you for this! The explanation was quite helpful and concise!

[@WrathofMath]

You're welcome, so glad it helped and thanks for watching!

[@darioarriaga7769]

love how you´re passionate about math thanks man

[@WrathofMath]

Thank you for watching, Dario! I love mathematics, and I love teaching it! Let me know if you ever have any video requests!

[@luisalcaraz9090]

Why has the internet been hiding you from me!? I’m so glad I came across your videos. Thank you! 😊

[@movierecap8355]

Am kindly requesting for complicated ellipse practice questions. And perhaps a video on conic section and binomial expansion

[@marciecastello5319]

For what, would I need to know the math re: ellipses, ie, astronomy, building electronics/technology?

[@ayalewmekonnen2408]

Great explanation.

[@thegoodlydragon7452]

But you didn't explain what defines the foci as such. You just said they are two points, but how do we know where we must put the points?

[@ramesh.programming]

You have to find them with equation or otherwise they are given with the question. (Exam perspective)

[@mushyomens6885]

Bcos they are exactly that, 2 arbitrary points. Set of all points such that sum of their distance from the 2 fixed points(i.e. foci) is constant (=2a) makes an ellipse.

[@pythonprojectsforwindows6795]

What is the distance between the two foci? It is 2c, 2 times the linear eccentricity but what is it called? What is h, mentioned in wiki article but not named? (I have a formula for h, not in wiki article).

[@vishaltaneja3191]

Can we also find 2 points on minor axis such that sum of the distances of any point from those 2 points is constant.

[@aqua1918]

i used this video to advance study i love the summarization !!

[@WrathofMath]

Thanks for watching Hannah, I'm glad it helped!

[@johnguy1350]

Very nice, what is not shown is how an ellipse oval shape is broken down into 360 degrees, not easy to find anywhere on the web. It would be nice if you can make a video on this. Thanks

[@ngocn6477]

Hi. Thank you for the video. Your explanation is very simple and clear. There is this principle that I’m still confuse about. Why an oval is used to represent ellipse? If it were a rectangle, would that not be an ellipse? Is an ellipse an oval with those three conditions that make it an ellipse as explained in the video then?

[@saifeekhaan8314]

great way of explanation i'm expecting more of it

[@WrathofMath]

Thank you for watching and for the compliment! I’m always working on new lessons, let me know if you have any requests!

[@phenomenalphysics3548]

@@WrathofMath Complex Numbers. DO IT! 🙏 please?

[@WrathofMath]

I have a few videos on complex numbers here kzbin.info/aero/PLztBpqftvzxWqdAHiwkpmV8JHSfVoqtNl Is there a particular lesson on complex numbers you'd like to see?

[@phenomenalphysics3548]

@@WrathofMath thank you so much 😻🤗 Yes, the Eulers identity.

[@lemuelredoma868]

Can you pls list at list five objects of the conic ellipse

[@RahulKumar-mg6nj]

video helped me to understand Kepler's law of planetary motion. thanks🙃

[@WrathofMath]

Glad to hear it, thanks for watching! I'm just about to get to Kepler's Laws in my multivariable calculus class - good stuff!

[@olivia-bu7os]

This helped so much thank you!

[@WrathofMath]

My pleasure, thanks for watching!

[@basimmahmood3935]

This is very clear, well done

[@WrathofMath]

Thank you! Glad it was clear!

[@schanzabukhari6064]

Studied this for the frist time and my concepts are perfectly clear! Thank you!

[@WrathofMath]

Thank you very much for watching and I am glad it helped!

[@sushantgupta4757]

thank you sir

[@talenthunt921]

I need more explanations. Like equation of ellipse and from the equation of elips how to find foci and equation of diretrix

[@hassanlearning4086]

Very helpful. Thank you.

[@WrathofMath]

Glad to hear it, thanks for watching!

[@rachaelgreen442]

What software are you using to make this video? Love it!

[@WrathofMath]

Thanks for watching, Rachael! The software I am using to write is "Notability" for iPad; it's a very wonderful app! Some of my more recent lessons also use Notability but with a black background instead of the notebook-looking background in this video, I think that looks good as well!

[@nagasaich5574]

I perfectly understand this explanation. 😊😊😊😊

[@WrathofMath]

So glad to hear it, thanks for watching!

[@krishna-ox3lj]

THANK YOU SO MUCH !

[@WrathofMath]

Glad to help, thanks for watching!

[@jenelynduena3342]

Thank yOu .I now clearly understand what ellipse is

[@WrathofMath]

Glad to hear it, thanks for watching!

[@Hallandfan847]

Thank you

[@abdiazizmadaale8679]

I'm from somalia east Africa I studed more from this lesson Thnk u so much..

[@WrathofMath]

You're very welcome and I am so glad it helped! Thanks for watching!

[@Ryamseyworld]

Iam from nepal..thank you my all doubt is clear

[@bagiaruna4708]

Thanks for the nice explanation

[@WrathofMath]

My pleasure, thanks for watching!

[@siidcalimaxamuudcali9668]

Well done.

[@WrathofMath]

Thank you!

[@judywillis792]

Loved it. Thx!

[@WrathofMath]

You're welcome, thanks for watching!

[@arnnmac7692]

Bro its easy so easy to understand after watching this!

[@WrathofMath]

Glad to hear it - thanks for watching!

[@Aman-jq3bw]

Sir, make some videos on parabola and hyperbola.

[@harmeetsindhkar5854]

Excellent👍

[@WrathofMath]

Thank you!

[@loading9357]

Epic video!

[@WrathofMath]

Thank you!

[@prashanthguntimadugu7186]

Very helpful sir Thank you

[@WrathofMath]

You're welcome and thanks for watching! I'm glad it was helpful!

[@bey6373]

How can ellipses be defined in relation to their foci?

[@nagasaich5574]

Super bro

[@n7s134]

excellent!

[@WrathofMath]

Thank you for watching!

[@shahandilhara8153]

How to find center to f1 distance

[@spindriftdrinker]

Holy Halibut Batman ! This guy is a GREAT math teacher ! Woo hoo, KZbin can be great if you get lucky and stumble upon him !

[@gabrielDMC01]

So can we get a visual description of a total solar ellipse???

[@anthonychikwalila4826]

You're appreciated

[@WrathofMath]

Thank you, Anthony!

[@fatkozi3817]

Thanks 💗

[@WrathofMath]

My pleasure, thanks for watching!

[@lifemalayalamyoutube7192]

Thanku sir🙏

[@WrathofMath]

Glad to help!

[@brajendrapandey4931]

Can you provide a video on parabola and hyperbola?:) Moreover, it's a nice video

[@WrathofMath]

Thanks for watching and for the requests! I'd love to help, is there something specific you're looking for regarding the parabola and hyperbola? There is a lot to be said about both items! I have one video on parabolas: kzbin.info/www/bejne/fpW0cmtqmtahoq8

[@brajendrapandey4931]

@@WrathofMath Can you just give an introduction, because, I like the way you try to introduce new things to us.

[@siidcalimaxamuudcali9668]

@@WrathofMath

[@immanuelvanlalawmpuia6070]

The owner of this video or someone, how will i know the vertical and horizontal in the question, tell me ASAP because in vertical, 'where a < b, and horizontal also, 'where a < b' is written the same. I don't understand this part where on how to identify the vertical or horizontal ellipse because it is important for me, tell me ASAP. I wish youtube had a camera in these comments too to show you what i do not understand

[@siya6349]

SIR, wanting more content over this ellipse chapter fully ,with all formulae and also with examples .....

[@WrathofMath]

Thanks for watching and for the request! A lot of people have asked for more lessons on ellipses, I am working to make some more soon!

[@siya6349]

thanks for the reply sir .. also thanks for working on ellipse topic !

[@letscrackcee18]

God bless you sir 🙏

[@WrathofMath]

Thank you for watching! Let me know if you ever have any questions!

[@cerainxjam1259]

nice one

[@WrathofMath]

Thank you!

[@JahanAcademy]

nice

[@WrathofMath]

Thank you!

[@abhijitroy3854]

Why ellipse has two focus?

[@andromedasdaughter1962]

I download this video from Africa Ethiopia

[@reignhard4696]

thank

[@WrathofMath]

welc

[@prathmeshzade7624]

Oval doesn't exist...hmmm What about eggs 🤔

[@WrathofMath]

Haha, that's a fine question! I think she may have said ovals don't exist partly because, as wikipedia says: "The term oval when used to describe curves in geometry is not well-defined", whereas ellipse is! In 3-dimensions, the oval shape is called an ovoid, so that is what the egg is!

[@royalstars2091]

I need more

[@WrathofMath]

Thanks for watching! Do you need me to clear anything up from the lesson?

[@royalstars2091]

@@WrathofMath I need eamcet maths classes

[@-EE-GIRIDHAR]

Solve some PROBLEMS on ellipse So that we can understand more clearly

[@AbrarManzoor]

Allah bless you

[@WrathofMath]

Thank you for watching!

[@qvipin]

Man u still active

[@WrathofMath]

Is that a question or a remark? I am still very active, check out my newest math rap! kzbin.info/www/bejne/iYPQZZydeNl9eck

[@qvipin]

@@WrathofMath IDK just asking my math teacher gave me ur vid so I got curious

[@blazor907]

5:21 What's the pun?

[@WrathofMath]

The pun was me using the verb focus, to say we needed to direct our attention to the focii (noun which is focus in the singular) of the ellipse.

[@qiwunu]

Lol its weird I understand this.. BUT i’m a 5th grader. Its just cool to watch this.

[@WrathofMath]

That's great you understand it! Thank you for watching!

[@evelyndominguez2443]

CONFIRMED

[@BennoRob95]

I’m starting to think an Oval is a rounded one-sided 2D shape that doesn’t follow the 2a rule

[@GregorySerrano1986]

Why is the distance called 2a? Where did the a come from? This is the question that everyone in my class keeps asking... and the teacher just says, "because that's what it is..." (' -_-)

[@WrathofMath]

Thanks for watching and great question, Gregory! Remember the semi-major axis has a length that is half our distance. By saying the distance is 2a, we are essentially saying "let the semi-major axis have length a". For a similar example, we might call the diameter of a circle "2r", and in doing that we have described the length of the radius as r, because the radius must be half the diameter. Does that make sense? We could just call the distance a if we wanted to, but by calling it 2a, we are "assigning" the length a to the semi-major axis (since its length is half the distance 2a), which is then helpful for various ellipse calculations. If we instead called the distance a, then the semi-major axis would necessarily be (1/2)*a. That would be fine too, but possibly less convenient.

[@mohamedalnaser501]

HI KALB

[@lealindelatorre8130]

came here to understand my math class not to see dnf ships

[@author_unknown654]

😁

[@WrathofMath]

Thanks for watching!

[@frankkarzenowski2385]

What's the purpose tho . Looks like an egg and number doodles

[@WrathofMath]

Thanks for watching! What's the purpose of what? The purpose of this video is to introduce the viewer to the shape and some of its features. Why study ellipses? Ellipses are a naturally occurring shape, for example the planets orbit the sun in an ellipse, with the sun's center as one of its foci. So to understand the planets' orbits about the sun, an understanding of ellipses is necessary. And yes - they do look like eggs!

[@abdullahalshaikh7546]

I still don’t get why it’s 2a

[@Vowbreaking]

شوف بما ان 2a اذا من الطرف الأيمن الى نقطه المركز =a, ومن الطرف الايسر إلى نقطة المركز ايضا يساوي a اذا من اليمين إلى اليسار =a+a=2a

[@robloxiancitizen4500]

E

[@WrathofMath]

Thanks for watching!

[@canomalo3662]

Worse explanation ever

[@DrewFeighner]

I bet yours would be worse

[@smileitsfreeanditwillmakes4121]

Didn't learn anything you talked in circles I hope you dont plan on teaching 1000s of others did a better job explaining this

[@WrathofMath]

circles? this video is about ellipses

[@user-lh4dy6hn3y]

Thank you

[@WrathofMath]

My pleasure, thanks for watching!