Deriving the equation of an ellipse

Deriving the equation of an ellipse from the property of each point being the same total distance from the two foci.
Used as an example of manipulating equations with square roots.

[@profmariogutierrez]

Exactly what I needed! Thank you!

[@alphalunamare]

You just made my day. I couldn't sleep the other night and tried working it out in my head. It didn't occur to me to split the two roots on either side of the equation. I fell asleep frustrated I recall. I google this result and up popped your method, exactly what I was trying to try :-)

[@alphalunamare]

Essentially I knew that I could construct ( no string ) an ellipse with just ruler and compass based on the sum of radii being a constant then it would be possible algebraically. Cheers! :-)

[@sanyammandot1953]

Thank you so much sir for explaining this derivation ...step by step👍👍....I am from India....honestly....I liked your proof of this derivation .....superb....great....👍👍👍👍👍👍

[@DLBmaths]

If you mean how do you differentiate this equation - then you will need to use 'implicit' differentiation to find the value of the derivative (gradient) at any point.
So in this case just differentiate each of the 3 terms.
2x/a^2 + (2y/b^2)dy/dx = 0 , put in the values of x and y at the point where you want the tangent, and that will give you the value of dy/dx, ie the gradient.

[@charityalexisolalia1774]

Thank you so much Sir, im really having a hard time understanding math. A Very big help to my assignment

[@silva2silver]

This was extremely helpful. Thank you so much.

[@s7d788]

Thank you so much. For some reason profs and books like to skip this derivation

[@nanaiahbm9503]

Thank you so much sir

[@nikitham6023]

Thanks a lot it helped me during my exam

[@prathimaumesh659]

Best explanation 💖

[@anuanu2483]

Tnq so much this video help me a lot ❤👌

[@jameswaswa9036]

Thank you sir🙏

[@physicsweb8697]

Really appreciable

[@amirazohair7620]

Thank you that was great

[@immanuelmaria7922]

Really helpful!!!!thank you

[@aeronauticsphantom]

How do you derive this equation? I need to find it's tangent.

[@lalah3372]

Genius! Thank you :)

[@andibunny5213]

How about if the center is at (h, k)? How do I derive the equation? Can you show me?

[@ゾカリクゾ]

lol

[@juliegarg1056]

How pc1 +pc2 =2a

[@jachpriboi2580]

Thank you sooooo much!!

[@darktechiez5421]

How does the value hypotenuse became a??

[@darkorandjic5308]

The sum of distances from any point to the foci is 2a. This applies to the point (0, b), interesingly when we connect the foci with the point we get an isosceles triangle, where the two equal sides are the distances from a focus to the point. Since they are equal and the sum of their lengths is 2a, each length must be a.

[@sonuvic]

Thanks a lot

[@ibrahimi3221]

thnk u sooooooooo much

[@DioD3]

excellent

[@shivaavr6465]

thankyou sir

[@dvgmanojff2406]

Tq...

[@guitarttimman]

Now, here's a fun one! You know how to use the disk method, some call it the onion method, with integral calculus to prove the volume of a sphere is 4/3 (pi)r^3. Do that for ellipse. It's fun! LOL

[@sirfuzzy96]

thank you :D

[@guitarttimman]

Yeah, that's a lot of work.
I was trying to get around all of that, but it's pretty much the only route.
But, at least the Parabola Equation, Y^2 = 4PX is easy to prove. LOL

[@moondanceff]

thank you good sir!

[@liamanderson6424]

Can you please go backwards now ???

[@jachpriboi2580]

Thank you sooooo much!!