Working out (deriving) equations for ellipses



I used this video for a lot more understanding:

These steps are just me following what's in the video

This is following something we did in class last year, and it relates the other form for an ellipse to the equations that we use on Hopscotch :slight_smile::

Then I was trying to explore more things, which maybe I don't know if I'll post (hasn't amounted to anything haha).

Nerdy Maths topics [check 'em out here!]

That's a lot of math! Woah. I hope u make an eclipse


Aw it looks like a lot because my writing is big, but it is in the video! Hehe thanks :sunny::new_moon: (I am just joking with those emojis :upside_down:)

I was thinking about approaching rotated/tilted ovals with maths so that is why I was doing horizontal ellipses before (and that is what I meant when I hadn't gotten much far) :slight_smile:.

This is the general idea I was having:


I donut understand 100% of this


I know right


Hey, just learned ellipses! I somewhat know this stuff
Let's do a part about circles and hyperbolas since they're very similar


Oooh yes!

i put some basics here (don't cover everything e.g. Hyperbolas with the y² part first, semicircles etc)


Nice, sounds good
(Also, Numberphile just posted a new video, posting it on the topic!)


Aw I see it seems very confusing – I don't want it to be alienating :cry: that is why I put the video which explains a lot better too :smiley: but hmm I am lacking a lot more explanation.

I was just putting this for anyone who was curious in working out how we get the Hopscotch equations but it is in a bit more depth


We watched that video in Geometry class like 4 days ago XD

We're learning about ellipses (and conic sections in general), if you're wondering.

Edit: I've been wondering the equation for a rotated ellipse... :thinking:
I was going to use it one time


Ooh :smiley:

(They just gave us the formula with no explanation of the derivation .-. so that is why I looked it up and how I found it)

And there are other topics with equations:

But i was curious in deriving something mathematically :upside_down:

I think there are a few things floating around:

And I was working through something and could see somewhat that what I was doing might lead to the first answer in that stackexchange link (I need to rewrite my working out if I show it though because it'd be illegible)

Anyway that's why this topic is here hehe, feel very free to join in :slight_smile:


This was where I started, after that diagram of the tilted ellipse earlier:

in Hopscotch we're using parametric equations so I tried doing the same for that stackexhange answer but didn't get very far hehe