Eccentricity of an Ellipse

This calculus 2 video tutorial provides a basic introduction into the eccentricity of an ellipse. It explains how to calculate the eccentricity of an ellipse from a standard equation. The eccentricity is close to zero for ellipses that are nearly circular and close to 1 for elongated ellipses.
Conic Sections - Free Formula Sheet:
bit.ly/4fyZTWA
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Conic Sections - Basic Introduction:
• Video
Finding The Radius and Center of a Circle:
• How To Find The Center...
Writing Equations and Graphing Circles:
• Graphing Circles and W...
Writing Equations of Ellipses:
• Writing Equations of E...
Circumference of an Ellipse:
• Circumference of an El...
Area of an Ellipse:
• Area of an Ellipse
____________________________
Eccentricity of an Ellipse:
• Eccentricity of an Ell...
Hyperbolas - Conic Sections:
• Hyperbolas - Conic Sec...
Parabolas - Focus and Directrix:
• Finding The Focus and ...
How To Find the Vertex of a Parabola:
• How To Find The Vertex...
Conic Sections Quiz:
• Conic Sections Quiz - ...
_____________________________
Arithmetic Sequences:
• Arithmetic Sequences a...
Geometric Sequences:
• Geometric Series and G...
Probability - Basic Intro:
• Introduction to Probab...
Intro to Statistics:
• Introduction to Statis...
Final Exams and Videos Playlists:
www.video-tuto...

[@TheOrganicChemistryTutor]

Conic Sections - Free Formula Sheet: bit.ly/4fyZTWA
Ellipses Mega Review: ruclips.net/video/_BuUMQAFWmI/видео.html
Hyperbolas Full Review: ruclips.net/video/aBednvA7rSY/видео.html
Parabolas Full Review: ruclips.net/video/7dH24WsuGsM/видео.html
Conic Sections Quiz: ruclips.net/video/vqZO_CrEdPs/видео.html
Next Video: ruclips.net/video/Mw3MeDLL8d4/видео.html

[@loryn7662]

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

[@ninwithabin2683]

are you in college

[@LoneCrusader1]

@@ninwithabin2683you can learn this in high school....

[@MARYOGBURN]

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

[@georgesadler7830]

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 RUclips TV with the Organic Chemistry Tutor.

[@scmtuk3662]

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

[@chinanumberone7723]

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

[@elbyful9750]

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

[@scottbarber9374]

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

[@lorrimartin6129]

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.

[@bwh.]

OMG thank you for the clarification. I kept on putting a under x even if it was smaller so I would get the eccentricity wrong if the ellipse was longer on the y axis.

[@heetdoshi1975]

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

[@Doraemon-ku5by]

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

[@lackinglactose2805]

This was amazing! Thx

[@LuxuryIncorp]

I came in confused and I left partially confused

[@ballermemesarebad]

I like the quiet background

[@VictorBarnabas-gl9dk]

I literally just watch your video one day to the CAT

[@anilkumarsharma8901]

Eccentricity show⌚ what 📈graphic level😀😀😀

[@gregheffeley4922]

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

[@Gataroes]

fucking nerd

[@gregheffeley4922]

Brodersen no u

[@papajon7789]

Brodersen you troll go back to Xbox 360’s chat were you belong

[@VaporSpaceNumber101]

@@papajon7789 boomers be laughin at this

[@shellssoul]

@Eric Arias WOOO GO ERIC!!! dont listen to him bruh hes just mad. embrace ur gifts and hobby :-). May God be with u always

[@piano_a2892]

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

[@santhoshkumarvirat6973]

Insta id

[@ScorpionYTS]

What if b is bigger than a? 😁

[@zeroanims4113]

Then we get a vertical major axis

[@harshpatil3616]

Then it is a conjugate ellipse

[@cileong]

a is always larger than b, if it's not, then the number below y becomes a², the number below x becomes b², so they basically switch places.

[@nagamanip1487]

@@cileong thanks

[@Name-yu6ux]

Vertical ellipse

[@nagamanip1487]

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

[@lukasnegumbo1879]

There is NO such a case

[@phenomenalphysics3548]

When a

[@brd8764]

About curves and free movements.

[@stanky5187]

what would it look like if eccentricity was somehow 1?

[@kunaljaju646]

parabola

[@pepsi_cann]

How does one manage to make this more confusing?

[@freeshorts4423]

What If e>1?

[@Abhilashaisgood]

Its a hyperbola then

[@navuliacallis1472]

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 😭

[@scmtuk3662]

Does (5 ^ 0.5) / 3 work?

[@jessicahass6198]

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

[@insaneasylum4845]

I just wanna say stfu

[@bigdaddychester8132]

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

[@Name-yu6ux]

Fr nigga

[@justinefetilo7083]

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

[@ryangendels6517]

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

[@abzuck5043]

When x^2 is 25 y^2 is zero. I don't see any mistakes there

[@ryangendels6517]

I see what you mean. Thank you

[@Doraemon-ku5by]

a and b are not x and y.
And on graph you can only put the value of that coordinate . Not the max of x and max of y . Bcz this will be outside of ellipse. So u can't put that value to equation of ellipse

[@MALAK-nn4rr]

شكرا

[@elliskestero5148]

First

[@hatelovebowel4571]

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

[@ZachStarAttack]

you're wrong screw you

[@MohammedramyCherif]

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