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 TH-cam 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
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.
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
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 😭
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So far this is the second class you’ve helped me pass
are you in college
@@ninwithabin2683you can learn this in high school....
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 TH-cam 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
Nice thanks . Keep it up 👍
Keep growing your channel.
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
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.
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.
This was amazing! Thx
I like the quiet background
"If e is exactly zero, then you no longer have an ellipse." Yes, you do. A circle is specialized ellipse.
I came in confused and I left partially confused
What if b is bigger than a? 😁
Then we get a vertical major axis
Then it is a conjugate ellipse
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.
@@cileong thanks
Vertical ellipse
Do you also teach in khan academy?
I think I have heard your voice in some lessons.
Insta id
About curves and free movements.
What If e>1?
Its a hyperbola then
what would it look like if eccentricity was somehow 1?
parabola
When a< b root value is negative know
So what is the method to find eccentricity in that case
There is NO such a case
When a
How does one manage to make this more confusing?
This is really easy and I'm in algebra 2/math 3 😊 I love math so much
fucking nerd
Brodersen no u
Brodersen you troll go back to Xbox 360’s chat were you belong
@@papajon7789 boomers be laughin at this
@Eric Arias WOOO GO ERIC!!! dont listen to him bruh hes just mad. embrace ur gifts and hobby :-). May God be with u always
I literally just watch your video one day to the CAT
this made no sense to me, symbolab eccentricity calculator made more sense..go use it
I just wanna say stfu
Omg 🤦♂️ I still don’t get this bull shit
Fr nigga
Isn't 25/25 + 1/1 = 2 not 1? Check that math again.
When x^2 is 25 y^2 is zero. I don't see any mistakes there
I see what you mean. Thank you
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
This just make the lesson more complicated.
Why didn't you square the a and b and just subtracted it?
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 😭
Does (5 ^ 0.5) / 3 work?
شكرا
First
Your videos never explain why and just plainly shove all the theorems in. It is truly terrible.
you're wrong screw you
You can't imagine how grateful I'm I right now, you helped me a lot that you so much 🤍🤍🤍🤍