same here, this saves a lot of time, tbh, why not just memorizing the final outcome but this animation is so good it makes me start to memorize the algebra computation.
This video is REALLY well done: the clear explanations, the showing of each step, the color coding, the image with the labels, the animations. I am so grateful to you and to so many others across the internet that share their knowledge. It has made a world of difference for me in my studies. Thank you.
reading all the articles online over and over does nothing to help me to understand the proof. But watching this just helps me to appreciate the simplicity and understand everything so much better.
The major axis was shown to be the entire length of the string. Half the major axis is a. Therefore, half the length of the entire string is also a. Remember, the string represents the distance from each foci (represented in this video by green dots) to the point. When the point is drawn at the top, the distance to the point from each foci is equal. Therefore, half of the string extends from each foci to the point. Since half of the string is a, the distance is a.
Thanks for the video! This makes so much more sense than how the teacher was trying to explain the derivation, and the animations of the steps really help. I can't tell you how many times I get lost in class when the teacher skips over the cancellations and such. I'll definitely keep looking at your channel for extra help! :)
O bijuterie de videoclip, atât de frumos și logic explicat, mai ales că în școală(liceu) nu prea s-a studiat elipsa. Practic e o problemă de loc geometric elipsa, adică punctul de coordonate (x,y), care satisface ecuația (x²/a²) +(y²/b²) = 1, cu "a" și "b" definite astfel încât a²=b²+c². Geometria analitică e foarte frumoasă. Totul din jurul nostru e matematică. Creatorul e un matematician desăvârșit. Succes în continuare. Vă urmăresc ori de câte ori am puțin timp. Sănătate, fericire și succes în continuare.
i prefer x²+y²=r², x²/r²+y²/r²=1, substitute the rs for a and b to fit the formula, like, in the area, πr² becomes πab, and you can see it geometrically
Thanks so much with this video! I didn't understand many of the variables and what they stood for, but this aw3some video made it really clear! Helped a lot!
Thankyou buddy, you actually simplified the equation by doing expansion and stuffs. I spent hours simplifying the equation and now i actually got it. Thankyou so much for the video. Love from India.
You really saved me dude !! I hadn't understood a single thing about this equation done in class. Finally I feel like I've solved a jigsaw puzzle . Thanks man ❤
This is so helpful Our teacher had told us that c² = a² - b² which us correct, but she also told us it was a rearrangement of the Pythgorean Theorem and didn't mention that in this case, the hypotenuse is actually a and not c like it usually is. Even in her explanations of it, she kept using the c as the hypotenuse, so it kept confusing me.
Dios Mio! I had been learning the derivation of the ellipse formula on a lecture material for half an hour until i watched your video! This gave me an enlightenment! Thank you!
Hello !! First of all thank you for your effort to bring these contents together and visually represent them for us to grasp them intuitively . However i have a question for you !! ----> at 2 : 13 the algebraic solution you got seemed to be not working for me. I have tried dozens of algebraic tricks but i could not get it . Perhaps you have made the binomial expansion in a wrong way ? --> My version : ( a sqrt ( x + c ) ^2 + y ^2 ) ^2 = ( a ^2 + xc ) ^2 --> a ^2 x^2 + 2a^2 xc + a^2 c^2 + 2 ( a ( x + c ) y ^2 ) + ( y^2 ) ^ 2 ---- > BINOMIAL EXPANSION . This is the left part of the equation i did not type the right part because this is where i kept looping back to the same point where i ended up checking the validity of my solution ---> Your version : a ^2 x ^2 + 2a ^2 xc + a ^2 c ^2 + a^2 y ^2 ---- > You seem to get " a ^2 y ^2 " but i did not get it how you made it I would be in debt if you reply back to me. Sincerely, your follower !! :) ..
+Can Coteli at 2:07 we have a*sqrt((x+c)^2 + y^2) = (a^2 + xc)^2 when we square both sides we get a^2((x+c)^2 +y^2) = (a^2 +xc)^2 on the left side we have to distribute a^2 therefore we have a^2(x+c)^2 +a^2y^2 Hence this is where a^2y^2 comes from.
So i imagine the person who came up with this sat struggling trying to figure out how to get a clean equation with a and b and x and y easily identifiable
Excellent video! Could you please tell me how did you make such video containing moving symbols? I really love this approach to show equation derivations.
Is it true for ellipses that f1 and f2 need to b at equal distance from centre?...then only 2a will be obtained....i mean how to find the mid point of x axis...coz as much as i know, coordinate geometry was not known during Appolonius's era...
Wow, this is actually a great explanation. I loved the way you animated the rearranging of the formula at the end! well done.
appreciate the comment!
same here, this saves a lot of time, tbh,
why not just memorizing the final outcome
but this animation is so good
it makes me start to memorize the algebra computation.
This helped me a lot.....
Beautifully explained. The animations that were use for steps are giving a sense of clear visualisation and pleasure which stood out.
This video is REALLY well done: the clear explanations, the showing of each step, the color coding, the image with the labels, the animations. I am so grateful to you and to so many others across the internet that share their knowledge. It has made a world of difference for me in my studies. Thank you.
What are you doing now???? You must be so grown up mann
Simple and Straight to the point - Love it!
Awesome sir🎉 keep it up
It was very easy to grasp your concept ❤
reading all the articles online over and over does nothing to help me to understand the proof. But watching this just helps me to appreciate the simplicity and understand everything so much better.
This video rocks. The visuals really make it. Thanks 4 taking the time to do that u da best don't ever change!
I have one little question. How do we know that the hypotenuse of the triangle with b and c as the other two sides is equal to a?
The major axis was shown to be the entire length of the string. Half the major axis is a. Therefore, half the length of the entire string is also a. Remember, the string represents the distance from each foci (represented in this video by green dots) to the point. When the point is drawn at the top, the distance to the point from each foci is equal. Therefore, half of the string extends from each foci to the point. Since half of the string is a, the distance is a.
Most beautiful explanation of ellipse on internet
Thanks for the video! This makes so much more sense than how the teacher was trying to explain the derivation, and the animations of the steps really help. I can't tell you how many times I get lost in class when the teacher skips over the cancellations and such. I'll definitely keep looking at your channel for extra help! :)
O bijuterie de videoclip, atât de frumos și logic explicat, mai ales că în școală(liceu) nu prea s-a studiat elipsa. Practic e o problemă de loc geometric elipsa, adică punctul de coordonate (x,y), care satisface ecuația (x²/a²) +(y²/b²) = 1, cu "a" și "b" definite astfel încât a²=b²+c². Geometria analitică e foarte frumoasă. Totul din jurul nostru e matematică. Creatorul e un matematician desăvârșit. Succes în continuare. Vă urmăresc ori de câte ori am puțin timp. Sănătate, fericire și succes în continuare.
i prefer
x²+y²=r²,
x²/r²+y²/r²=1,
substitute the rs for a and b to fit the formula, like, in the area, πr² becomes πab, and you can see it geometrically
omg gracias
The derivation of the ellipse formula was awesome! More please!
This video is absolute MONEY! You have made it super easy to understand the formula for an ellipse. Excellent work and thank you!
This was sooo good! We need people like u so badly!
Words cannot express how grateful I am you just helped me to solve a problem that stuck in my head for dayzzz. Subscribed
First educational video I've seen on youtube.. Thanks
Thank you so much! It just clicked for me perfectly! 😊
this video is perfect, you even showed how ellipse is drawn, hence the reason why d1+d2=2a
@0:53, how do we know that such a triangle can be formed?
Absolutely beautiful. A bit fast, but easy to pause and keep going back.
Thanks so much with this video! I didn't understand many of the variables and what they stood for, but this aw3some video made it really clear! Helped a lot!
Ultimate sir!! Top class video !! No one can explain nicely like you within 3min 👏👏Thanks a lotttt🤝🤝
The title of this video didn't lie ❤
Bravo, I love your explanation, especially the sphere one.
:)
Phenomenal video. If only professors explained material the way you did
this is way more helpful than my math teachers
it took me 3 seconds to remember what is was. excellent video! just impressive!
Thankyou buddy, you actually simplified the equation by doing expansion and stuffs. I spent hours simplifying the equation and now i actually got it. Thankyou so much for the video. Love from India.
I feel bad for the poor mathematician who probably spent hours rearranging that formula.
DaveDonnie I wouldn’t feel bad, I honestly bet he had a blast
@@Schultzie580 yes, figure out ellipse equation after an endless rearrangement definitely a blast for me, it chills my spine ;)
Lol, I would have the time of my life rearranging that.
There's no pornhub back then.
My teacher made us do that..
Amazing video, I had my doubts with you labelling it "the best" explanation, but you proved yourself right! Thank you so much!
I had to wait a few years, but it works!
@@mathematicsonline Quite impressive that you made this 8 years ago, I'd imagine it was harder to learn editing like this back then
You deserve something great man, thank you so much for this, much love
You really saved me dude !! I hadn't understood a single thing about this equation done in class. Finally I feel like I've solved a jigsaw puzzle . Thanks man ❤
Best proof video ever, short and clear, with excellent amination! Keep up the good work!!
Thank you so much! It's sad how they never teach us these things in math and we always have to look it up ourselves
Very nice
This is so helpful
Our teacher had told us that c² = a² - b² which us correct, but she also told us it was a rearrangement of the Pythgorean Theorem and didn't mention that in this case, the hypotenuse is actually a and not c like it usually is. Even in her explanations of it, she kept using the c as the hypotenuse, so it kept confusing me.
5 years later and this is still saving Algebra 2 students
Great explanation and easy to follow and understand. Very helpful. Thank you
Absolutely perfect. Thank you
sir you are a blessing to humanity
Great explanation! Keep it up👍 please upload more videos about conic sections as soon as possible
Thank you for your outstanding explanation of the Equation of an Ellipse. How about an explanation of a hyperbola?
Dios Mio! I had been learning the derivation of the ellipse formula on a lecture material for half an hour until i watched your video! This gave me an enlightenment! Thank you!
It is short but seriously it is an absolute video. Thanks a lot.
What a wonderful explanation, loved it.
it was very nice... how did u do that animation in equation solving ???
Absolutely beautiful. I love how you show the proofs!
Excellent video just in 3 minutes all things are explained
Can you make a video about deriving the formula of the hyperbola?
Once you know how to derive the eqn for ellipse then it's simple. Use the property D1-d2=2a for hyperbola and so on
i love these videos, only makes math even more amazing
wow, you explained that better than my astrophysics professor. Very well done.
Thank you I'm trying to solve line / ellipse intersection and this was very informative on what ellipse formula to use.
Thanks, I am searching for it's Simplification of its equation . You did a great job
you saved me for my math hw bless ur soul
Thank you so much !! I wish my math teacher explained where the formula came from. This video is very well made and very helpful
Hello !! First of all thank you for your effort to bring these contents together and visually represent them for us to grasp them intuitively . However i have a question for you !!
----> at 2 : 13 the algebraic solution you got seemed to be not working for me. I have tried dozens of algebraic tricks but i could not get it . Perhaps you have made the binomial expansion in a wrong way ?
--> My version : ( a sqrt ( x + c ) ^2 + y ^2 ) ^2 = ( a ^2 + xc ) ^2
--> a ^2 x^2 + 2a^2 xc + a^2 c^2 + 2 ( a ( x + c ) y ^2 ) + ( y^2 ) ^ 2 ---- > BINOMIAL EXPANSION . This is the left part of the equation i did not type the right part because this is where i kept looping back to the same point where i ended up checking the validity of my solution
---> Your version : a ^2 x ^2 + 2a ^2 xc + a ^2 c ^2 + a^2 y ^2 ---- > You seem to get " a ^2 y ^2 " but i did not get it how you made it
I would be in debt if you reply back to me. Sincerely, your follower !! :) ..
+Can Coteli at 2:07 we have a*sqrt((x+c)^2 + y^2) = (a^2 + xc)^2
when we square both sides we get a^2((x+c)^2 +y^2) = (a^2 +xc)^2
on the left side we have to distribute a^2 therefore we have a^2(x+c)^2 +a^2y^2
Hence this is where a^2y^2 comes from.
This is exactly what I'm looking for, thank you ❤️
Explained fantasticly!👌
Thanks..... Love from India!!
What algebraic formula you used for [a sqrt(x+c)^2+y^2]^2
0:28 how do you know it?
Know what? Those are just names for the shortest and longest sides.
How did you cancel the three 4 on 2:06 ? Did u use the divide to 4 or did u transfer the 4 to the other side thus making it a -4?
በጣም አሪፍ ነው እናመሰግናለን😁😁thanks
So i imagine the person who came up with this sat struggling trying to figure out how to get a clean equation with a and b and x and y easily identifiable
Nice Explanation 👍👍
Thank you sir,you helped me a lot to clear a very big calculation and concept.
This is great explanation! Is it there in slides or step by step calculation format? Thanks, a really good explanation but went a bit faster !
I love the explanation!!! Like.. this is the great vid for tutorials.. like it very much
Wait is this the area or circumference or the volume of a ellipse
Absolutely Informative
this is absolutely longer than my patience but thanks!!! your explained it so well :))
i hope you make more videos. this helped alot
Wow is awesome! You give the perfection to the geometry
I love you I was trying this for an hour,a solid hour ;-;
Amazingly good animation. I needed the last step to be a bit slower to follow.
Bro, thank you for this video. May I know what software did you use for this video and animation?.. Thank you.
Excellent video! Could you please tell me how did you make such video containing moving symbols? I really love this approach to show equation derivations.
Nice calculating of proofing formula of ellipse
Thank you
Man, you are great. Hats off.
Very clear! Thank you.
Excellent Excellent EXCELLENT Video!!!! thank you!!. great production value and Definitely a Learning Experience!! the best I've seen!!...
Really great 👍
at 0.55 hows that length of hyp is a
Amazing explanation I like last evoution of equation TQ sooo much
Yes its really good explanation. It was quite easy to understand.
thank you for the nice video.. You should add subtitle ( without auto generating) .. it is very much helpful for non english speakers
THANK U SO MUCH ..
IT HELPED ME A LOT IN MY EXAM
Dude, that was amazing! THANK YOU!
Uhhh how do you get 4a^2-4a.....? it said to square both sides but how did 2a got another 4a???
Your explanation is incredible! Reminds me of 3Blue1Brown
Thank you, this video helped me so much
Wow!!! And do you have the derivation of the eclipse along the y axis??? ❤️
Is it true for ellipses that f1 and f2 need to b at equal distance from centre?...then only 2a will be obtained....i mean how to find the mid point of x axis...coz as much as i know, coordinate geometry was not known during Appolonius's era...
Nicely explained
perfect example of simple but elegant!
Could you derive the area of an ellipse like you did with the circle?
Very good explanation .. Thank you .
I really thought it has something to do with geometry