Eccentricity of an Ellipse 

Ellipses Mega Review: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-_BuUMQAFWmI.html Hyperbolas Full Review: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-aBednvA7rSY.html Parabolas Full Review: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-7dH24WsuGsM.html Conic Sections Quiz: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-vqZO_CrEdPs.html Next Video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Mw3MeDLL8d4.html

So far this is the second class you’ve helped me pass

love his voice and the fact that he talks slowly and calmly!

Professor Organic Chemistry Tutor, thank you for a short and well explained video/lecture on the Eccentricity of a Basic Ellipse in Calculus Two. The practice problems/examples are easy to follow and understand from start to finish. This is an error free video/lecture on RU-vid TV with the Organic Chemistry Tutor.

Thanks so much for this video, I saw eccentricity in a past exam paper, and I didn’t know how to do it, even tho it’s year 12 extension 2, and I’m only year 11 extension 1 currently, I’ll watch more of your videos that relate to the paper, so I can try it out and hopefully go well for practice

The "definition" of "eccentricity" is: "the ratio of the distance from the center to a focus divided by the length of the semi-major axis" The "focus" is "the square root of the difference between the squares of the semi-major and semi-minor axis". The semi-major axis, is the longest radius of the ellipse, and the semi-minor axis is the shortest radius of an ellipse. This means, if you have an ellipse where the longest radius is 36, and the shortest radius is 16: The focus would be √(36² - 16²) = √(1296 - 256) = √1040 = 32.2490309932. Therefore, the eccentricity, is the ratio of the focus (32.2490309932) and the semi-major axis (36), which is 32.2490309932 / 36, which is 0.89580641647. If the semi-major axis however is _really_ big, e.g. 1 billion, and the semi-minor axis is very small, like 2, then: The focus is √(1,000,000,000² - 2²) = √(1,000,000,000,000,000,000 - 4) = √(999,999,999,999,999,996) And if you divide √(999,999,999,999,999,996) / 1,000,000,000, you'd get a number that is _very_ close to 1. Something like 0.999999999999999998. Meanwhile, if the semi-minor and semi-major axis are equal, for example, 9, then: The focus becomes √(9² - 9²) = √(81 - 81) = √0 = 0 Therefore, the eccentricity becomes 0 / 9 = 0 Therefore, it is a circle. The general formula for eccentricity is e = [√(a² - b²)]/a

thanks so much you changed my life with your videos I would've never passed precalc in my junior year of college without your gracious gifts of teaching along the way thanks so much

thank you so much sir! was very confused with eccentricity but finally understood. thnx

Nice thanks . Keep it up 👍 Keep growing your channel.

It would have been good to have an example where a^2 is under y^2 to remind them that it's always the larger number that is a, not the smaller.

This was amazing! Thx

I like the quiet background

This is really easy and I'm in algebra 2/math 3 😊 I love math so much

About curves and free movements.

"If e is exactly zero, then you no longer have an ellipse." Yes, you do. A circle is specialized ellipse.

Do you also teach in khan academy? I think I have heard your voice in some lessons.

When a< b root value is negative know So what is the method to find eccentricity in that case

I came in confused and I left partially confused

what would it look like if eccentricity was somehow 1?

What If e>1?

What if b is bigger than a? 😁

How does one manage to make this more confusing?

Eccentricity show⌚ what 📈graphic level😀😀😀

Please someone answer me Our quiz is tomorrow And I still cant figure it out How to do squareroot of 5 divided by 3 on a scientific calculator. Everytime i do it, it always shows " 1 " and not 0.745 😭

I literally just watch your video one day to the CAT

شكرا

this made no sense to me, symbolab eccentricity calculator made more sense..go use it

This just make the lesson more complicated. Why didn't you square the a and b and just subtracted it?

Isn't 25/25 + 1/1 = 2 not 1? Check that math again.

Omg 🤦‍♂️ I still don’t get this bull shit

First

Your videos never explain why and just plainly shove all the theorems in. It is truly terrible.

You can't imagine how grateful I'm I right now, you helped me a lot that you so much 🤍🤍🤍🤍