Recent content by Adwit

Here is my own effort. Now, will you please tell me where I went wrong? What do I have to do?

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

Ok, this is the last time I posted image of calculation. For now, I will write the calculation. Now, can you do the steps between 3 no. equation and 4 no. equation ?

I understand how do 3 no. equation come from 1 & 2 no. equation. But I am struggling to understand how do 4 no. equation come from 3 no. equation. Will anyone do the steps between 3 no. equation and 4 no. equation, please ?

In the picture, ρ is not written. I didn't know either ρ is the connector line from the origin to point B or A or it is any other line ? I didn't know which line is ρ . I wanted to know which line indicates ρ .

Of course, distance is a thing you can see. When I draw a line which connects two points, that line is the distance either it is in hyperbola or circle. That is what I mean by saying " we see distance". Understand? That pictured line is the distance. Everybody in the world thinks that the...

Gaussian97 , In the case of circle geometry, we see distance r. Where is the distance ρ in hyperbola picture? Is it from the origin point to point B ? Now I hope you understand my question.

Gaussian97, Of course, there was math to be done. This is the math.

vanhees71, I know your math. I just want to know where is ρ in the picture of the hyperbola ? In the case of circle geometry, we see distance r. Where is the distance ρ? Is it from the origin point to point B ?

I do the math. Constant becomes 1. But the screenshot of my question shows that constant is some kind of squared distance ρ ^2. Can you show me where is this distance in the hyperbola picture?

Don't bring special relativity or any physics ( ct or Lorentz transformation ) in here. I want to see the problem from the mathematical perspective, not physics perspective. Where do I find the derivation of distance formula of hyperbola? Forget physics. How do I derive it mathematically?

Can anyone derive the distance formula of a hyperbola for me, please? I have not found the derivation on the internet. I can't get any clue from the picture of hyperbola.

With all due respect hilbert2, isn't the plus sign of 1st "sinϕ expansion" actually going to be minus sign? I indicate it with red colour. By the way, thanks for your explanation.

What does it mean ? I recognize phi. But what is this symbol that looks like O ? I have never seen this in my life.

How do "sinϕ - cosϕ sinϕ" become 0 ?