Function with same ratio between two points

[ebutyouyou]

Hi everyone, my first post and thread on this forum, hope you guys can help me
First of all, sorry for my English, it isn't that good.

I'm looking for a function, that if you have two point, the distances from these points too a point on the fucntion always returns the same ratio of these distances.

I made this drawing to make more clear what i mean (paint ****yeah) . For every point on the red line the ratios of the distances should be the same, so D1/D2 = S1/S2 !

In the end I need to make a graph with 8 points(locations). 1 Point is the reference point, and i have determined a certain kind of coupling between those points ( the ratio I was talking about). Now i need to map al those ratios. Do you guys have any idea how to do this. I'm familiar with MatLab and a little bit with python

Thanks in advance for helping me !

 

[tkhunny]

If only it were clear what it is you are doing. Please be VERY specific and show YOUR best attempts.

 

[ebutyouyou]

Hi tkhunny !

Thanks for your answer, and sorry for the inconvenience!


I will try to explain better, by first giving an similar problem that is easy.
If you have a point , and a line. And you are looking for a function such that the distance from the point to that function is equal to the distance from the line to the function.
The function describing this problem is a parabola, see figure:




Now the problem I have:
I have two points, P1 and P2, and an associated ratio, say for instance a ratio M = 0,4 .
I am looking for a function that describes all the points x, such that M = |P1x| / |P2x|
Or ,in the manner is described before:
I am looking for formula that describes the red line such that for every point on the line: M= D1/D2 = S1/S2


Is there an analytical function that describes this function?

 

[tkhunny]

And p3 and p4?

 

[ebutyouyou]

P2 is my reference point. I have a ratio corresponding to P1 and P2.

I also have a (other) ratio corresponding to P3 and P2 , for which i also need a line.
Also one for P4 and P2, P5 and P2 and so on.
I only drew 4 points because I am lazy, and my first post was far from clear I see now, sorry for that.