What is an Ellipse? | Geometry, Ellipses Definition, Introduction to Ellipses
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- เผยแพร่เมื่อ 9 ก.พ. 2025
- 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!
+WRATH OF MATH+
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Can you explain sun position in the ellipse on how and where it got positioned?
Bro thank you so much for the video, you described it without sounding monotone and ur channel name is amazing lol.
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!
Glad to help - thanks for watching and good luck with 3d design!
great way of explanation i'm expecting more of it
Thank you for watching and for the compliment! I’m always working on new lessons, let me know if you have any requests!
@@WrathofMath Complex Numbers. DO IT! 🙏 please?
I have a few videos on complex numbers here th-cam.com/play/PLztBpqftvzxWqdAHiwkpmV8JHSfVoqtNl.html
Is there a particular lesson on complex numbers you'd like to see?
@@WrathofMath thank you so much 😻🤗
Yes, the Eulers identity.
Why has the internet been hiding you from me!? I’m so glad I came across your videos. Thank you! 😊
video helped me to understand Kepler's law of planetary motion. thanks🙃
Glad to hear it, thanks for watching! I'm just about to get to Kepler's Laws in my multivariable calculus class - good stuff!
Thank you for this! The explanation was quite helpful and concise!
You're welcome, so glad it helped and thanks for watching!
Holy Halibut Batman ! This guy is a GREAT math teacher ! Woo hoo, TH-cam can be great if you get lucky and stumble upon him !
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?
You have to find them with equation or otherwise they are given with the question. (Exam perspective)
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.
love how you´re passionate about math
thanks man
Thank you for watching, Dario! I love mathematics, and I love teaching it! Let me know if you ever have any video requests!
I'm so glad I found your video. Thank You for this sir!✨
I'm from somalia east Africa
I studed more from this lesson
Thnk u so much..
You're very welcome and I am so glad it helped! Thanks for watching!
Studied this for the frist time and my concepts are perfectly clear! Thank you!
Thank you very much for watching and I am glad it helped!
Really helpful for me....i understand concept.of ellipse..thnks ..❤....make more videos on another topics..😊
i used this video to advance study i love the summarization !!
Thanks for watching Hannah, I'm glad it helped!
Excellent👍
Thank you!
I perfectly understand this explanation. 😊😊😊😊
So glad to hear it, thanks for watching!
Great explanation.
Bro its easy so easy to understand after watching this!
Glad to hear it - thanks for watching!
Very helpful. Thank you.
Glad to hear it, thanks for watching!
Well done.
Thank you!
Thank yOu .I now clearly understand what ellipse is
Glad to hear it, thanks for watching!
Thanks for the nice explanation
My pleasure, thanks for watching!
THANK YOU SO MUCH !
Glad to help, thanks for watching!
All doubts are clear for me
Am kindly requesting for complicated ellipse practice questions. And perhaps a video on conic section and binomial expansion
This is very clear, well done
Thank you! Glad it was clear!
Bro can explain latus retum what is it and formula and end points of LR ,and what is focal chord,chord, directrix equation for parabolas 😊
God bless you sir 🙏
Thank you for watching! Let me know if you ever have any questions!
This helped so much thank you!
My pleasure, thanks for watching!
So can we get a visual description of a total solar ellipse???
Can you provide a video on parabola and hyperbola?:)
Moreover, it's a nice video
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: th-cam.com/video/HdQA84eqnlM/w-d-xo.html
@@WrathofMath Can you just give an introduction, because, I like the way you try to introduce new things to us.
@@WrathofMath
Sir, make some videos on parabola and hyperbola.
Very helpful sir
Thank you
You're welcome and thanks for watching! I'm glad it was helpful!
thank you sir
Iam from nepal..thank you my all doubt is clear
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?
SIR, wanting more content over this ellipse chapter fully ,with all formulae and also with examples .....
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!
thanks for the reply sir .. also thanks for working on ellipse topic !
Can we also find 2 points on minor axis such that sum of the distances of any point from those 2 points is constant.
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
Epic video!
Thank you!
What software are you using to make this video? Love it!
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!
excellent!
Thank you for watching!
Thanks 💗
My pleasure, thanks for watching!
You're appreciated
Thank you, Anthony!
nice one
Thank you!
thanks in advance love
thanks for watching!
Thanks sir all clear but calculations please 🙏🙏🙏
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
I need more explanations. Like equation of ellipse and from the equation of elips how to find foci and equation of diretrix
Thanku sir🙏
Glad to help!
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).
Loved it. Thx!
You're welcome, thanks for watching!
Can you pls list at list five objects of the conic ellipse
Super bro
Thank you
My pleasure, thanks for watching!
How can ellipses be defined in relation to their foci?
For what, would I need to know the math re: ellipses, ie, astronomy, building electronics/technology?
How to find center to f1 distance
I’m starting to think an Oval is a rounded one-sided 2D shape that doesn’t follow the 2a rule
I download this video from Africa Ethiopia
Oval doesn't exist...hmmm
What about eggs 🤔
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!
you mention the distance as 2a with saying from where to where? in the first place
came here to understand my math class not to see dnf ships
Very helpfull for me , becUse i am messing with the minkowski space , so i have to leran hyperbolic
Man u still active
Is that a question or a remark? I am still very active, check out my newest math rap! th-cam.com/video/SRm4igCtJCg/w-d-xo.html
@@WrathofMath IDK just asking my math teacher gave me ur vid so I got curious
thank
welc
nice
Thank you!
Lol its weird I understand this.. BUT i’m a 5th grader. Its just cool to watch this.
That's great you understand it! Thank you for watching!
Why ellipse has two focus?
Solve some PROBLEMS on ellipse
So that we can understand more clearly
I need more
Thanks for watching! Do you need me to clear anything up from the lesson?
@@WrathofMath I need eamcet maths classes
Allah bless you
Thank you for watching!
But what is braces
5:21 What's the pun?
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.
CONFIRMED
I still don’t get why it’s 2a
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
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..." (' -_-)
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.
HI KALB
What's the purpose tho . Looks like an egg and number doodles
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!
E
Thanks for watching!
😁
Thanks for watching!
Worse explanation ever
I bet yours would be worse
Didn't learn anything you talked in circles I hope you dont plan on teaching 1000s of others did a better job explaining this
circles? this video is about ellipses
Thank you