Apollonian circles, but then harder

ebutyouyou

New member
Joined
May 9, 2017
Messages
5
Hi everyone !

I have a problem, closely related to an apollonian circle. For those who are not familiar with Apollonian circles:
If given the points A&B, the points P such that AP/BP = M form an apollonian circle. So the ratio between the two distances is constant.
See also figure LocusCircle.jpg

.

Then there is the problem I've got:
I need to find al the points P, such that l1/s1=M . I've tried too draw this.
IMG_6590.jpg

I have calculated the points P that are on the line that goes through x1 and x2. This is just simply the quadratic ABC formula. But I have literally no idea how to continue.
I have tried working with coordinates but I didn't succeed.
EDIT: the only information I have, is the distance between the points d, the height h, and the ratio M.
Thanx in advance for helping me!
 
Last edited:
'h' is fixed? How many solutions are you expecting?
 
'h' is fixed? How many solutions are you expecting?

h is fixed.
I dont really understand what you mean by how many solutions i am expecting ?
I think there is one shape again that 'describes' all the solutions. I expect it to have an eggshape this time instead of a circle, but not sure about that.
Then, I expect 2 solutions on the line connecting x1 & x2, en already found those two solutions. For the whole shape I expect an eggshape
 
You have:

1) Fixed Base
2) Fixed Height
3) Fixed Ratio

Are you SURE there are more than 2 solutions?
 
Top