Ellipse and hyperbola equations from locus definitions

Рет қаралды 417

8 ай бұрын

Deriving equations for ellipses and hyperbolae from their definitions as loci of points such that the sum or difference of distanaces to two fixed points is constant. In the process, we also derive the Pythagorean relationships between the parameters a, b and c.
About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#mathematics #geometry #conicsections #loci #ellipse #hyperbola #equation #cartesian #curve #locus #algebra #pythagoras #physics #orbit #kepler #maths #math #science #education

Пікірлер: 10

@mxminecraft9410 8 ай бұрын

For a=0 , would it trace a path on +y axis ?

@DrBenYelverton 8 ай бұрын

For the hyperbola, a = 0 implies d₁ = d₂, so the locus is the entire y axis. For the ellipse, a = 0 implies d₁ and d₂ are both zero; this is only possible if c = 0 as well, and you get a single point at the origin.

@mxminecraft9410 8 ай бұрын

@@DrBenYelverton thx :)

@shaunakpillay986 8 ай бұрын

Hello sir can you make a video on minimum torque required to slide a ball out of a hole.

@DrBenYelverton 8 ай бұрын

Hello and thanks for watching. Could you give me some more details on the problem setup? Are you thinking of something similar to this: kzfaq.info/get/bejne/rbNjbJqDzN_al2Q.html ?

@mxminecraft9410 8 ай бұрын

Sir why haven't you uploaded in so long ?

@DrBenYelverton 8 ай бұрын

I haven’t had enough spare time to make videos for the last couple of weeks, hope to be back to posting within the next week or so!

@mxminecraft9410 8 ай бұрын

@@DrBenYelverton Ok can you make one on moment of inertia and rotational mechanics in Newtonian and lagrangian?

@DrBenYelverton 8 ай бұрын

That sounds like a very broad topic! I have some other videos planned but if you have some more specific suggestions I'll put them on my to-do list.

@mxminecraft9410 8 ай бұрын

@@DrBenYelverton ok :) Hope to see some videos soon