Maths Proofs, Videos & Tutorials

Search
Skip to content
  • Algebra
  • Trigonometry
  • Calculus
  • Vectors
  • Video Playlists
  • Navigation (Page by Page)
  • All Posts (Archives)
  • XML Sitemap
Algebra, Areas, Ellipses, Mathematics Proofs, Proofs

How to find a neat version of y when you have the equation of an ellipse

August 30, 2017 Tiago Hands

So, you have the equation of the ellipse but you need to completely isolate y. How would you go about doing this? Well, here is a fantastic example…

{ \left( \frac { x }{ a } \right) }^{ 2 }+{ \left( \frac { y }{ b } \right) }^{ 2 }=1\\ \\ \therefore \quad { \left( \frac { y }{ b } \right) }^{ 2 }=1-{ \left( \frac { x }{ a } \right) }^{ 2 }\\ \\ \therefore \quad \frac { { y }^{ 2 } }{ { b }^{ 2 } } =1-\frac { { x }^{ 2 } }{ { a }^{ 2 } } \\ \\ \therefore \quad { y }^{ 2 }={ b }^{ 2 }-\frac { { { b }^{ 2 }x }^{ 2 } }{ { a }^{ 2 } } \\ \\ \therefore \quad { y }^{ 2 }=\frac { { a }^{ 2 }{ b }^{ 2 } }{ { a }^{ 2 } } -\frac { { b }^{ 2 }{ x }^{ 2 } }{ { a }^{ 2 } } \\ \\ \therefore \quad { y }^{ 2 }=\frac { { a }^{ 2 }{ b }^{ 2 }-{ b }^{ 2 }{ x }^{ 2 } }{ { a }^{ 2 } } \\ \\ \therefore \quad { y }^{ 2 }=\frac { { b }^{ 2 }\left( { a }^{ 2 }-{ x }^{ 2 } \right) }{ { a }^{ 2 } } \\ \\ \therefore \quad { y }^{ 2 }=\frac { { b }^{ 2 } }{ { a }^{ 2 } } \cdot \left( { a }^{ 2 }-{ x }^{ 2 } \right) \\ \\ \therefore \quad y=\sqrt { \frac { { b }^{ 2 } }{ { a }^{ 2 } } } \cdot \sqrt { { a }^{ 2 }-{ x }^{ 2 } } \\ \\ \therefore \quad y=\frac { b }{ a } \cdot \sqrt { { a }^{ 2 }-{ x }^{ 2 } }

This will come in handy if you’re trying to derive the area of an ellipse from absolute scratch.

Thanks for reading! 🙂

algebraareasellipsesmathematics proofsproofs

Post navigation

Previous PostUseful trigonometric formulas for finding areas of circlesNext PostAnother way to express the golden ratio mathematically

Subscribe to our Youtube channel

Receive notifications about our latest clips as soon as they become available. We've produced some of the best GCSE and A Level mathematics proofs videos on the web.

Instagram Links

  • Tiago Hands (Geometric & Isometric Art)
  • Mathematics Proofs (GCSE & A Level)
  • Scientific Quotes (Randomly Selected)

Watch the Mathematics Videos Relevant to YOU

Our videos have now been categorised and dated, allowing you to watch the clips that are relevant to you – instantly. Get access to all the links to each of our 224 mathematics videos by clicking here. Searching for an article? See all our site tags.

Books for Study

Buy Edexcel A Level Mathematics Books via Amazon

Archives

  • November 2018 (1)
  • October 2018 (3)
  • September 2017 (4)
  • August 2017 (3)
  • July 2017 (7)
  • February 2017 (5)
  • January 2017 (1)
  • October 2016 (1)
  • September 2016 (7)
  • August 2016 (3)
  • March 2016 (1)
  • February 2016 (2)
  • December 2015 (1)
  • November 2015 (1)
  • September 2015 (2)
  • August 2015 (4)
  • July 2015 (1)
  • June 2015 (2)
  • May 2015 (1)
  • March 2015 (7)
  • February 2015 (7)
  • January 2015 (8)
  • December 2014 (29)
  • July 2014 (12)
  • June 2014 (4)
  • May 2014 (14)

GCSE + A Level Mathematics Proofs, Videos and Tutorials.

  • Home
  • About Us
  • Resources
  • Frequently Asked Questions
  • Philosophy
  • Edexcel A Level Mathematics Books
  • Magick 6 – 6 Fundamental Trigonometric Identities & Their Proofs
  • Product Recommendations – By TIAGO HANDS
  • All Youtube Videos
  • All Site Tags (Find Topic)
  • RSS Feed
  • XML Sitemap
  • Contact Us

Categories

Instagram Links

  • Tiago Hands
  • Mathematics Proofs
  • Scientific Quotes

Legal

  • Privacy & Cookies Policy
  • Learn more about cookies (Information Commissioner’s Office)
  • Terms Of Use
  • Disclaimer
Proudly powered by WordPress
We use cookies so that visitors can have a pleasant experience on our website. If you continue to use this site, we will assume that you are satisfied with our privacy and cookies policy.OkRead more