Hey guys,
I'm trying to find the foci of an ellipse. If you know the major and minor axis, this is easy.
I'm my case, I know the major axis and the radius of the ellipse.
Is there an easy way then to find the foci?
Thanks,
M
Edit: just realised there may not be a unique ellipse? Any opinions?
I'm still not understanding this. If r1 and r2 are the distances from a focus to the two ends of the major axis, then their sum will be the length of the major axis. So if you already know the length of the major axis, then knowing r1+r2 won't tell you anything new.
Agreed, but I think there may be another solution, specific to the specific problem I'm working on.r1 + r2 = 2a. So as already mentioned, you don't have enough information to uniquely define the ellipse.
I'm working on a kind of sonar problem. I'm transmitting a signal from one loudspeaker to a microphone. The signal is transmitted outwards, meets an obstacle, is reflected and recieved at a microphone, as shown in the diagram below:
I know the total distance from the loudspeaker to the obstacle and back to the microphone. The signal can't go behind the loudspeaker (to the right) or to the left of the microphone, so this makes it a special type of ellipse. I think the obstacles location is on an ellipse where the foci and the end points of the major axis overlap?!
I'm not sure, I just think there should be a unique ellipse for this problem?
Thanks
M
If the foci are at the ends of the major axis then the minor axis will be of length zero, and the "ellipse" will just consist of a line segment along the major axis. That obviously isn't the case here. The fact that the signal can't go beyond the microphone/loudspeaker just tells you that the reflector can only consist of part of an ellipse. But it doesn't tell you anything about the shape or eccentricity of the ellipse.
Do you know the distance between the microphone and the loudspeaker? If you do, then that will determine the shape of the ellipse.
If an ellipse has semimajor axis a and eccentricity e, then the distance between the foci is 2ae, and the length of the reflected path from one focus to the other is r1+r2=2a. In this case, the loudspeaker and microphone are situated at the foci. If the distance between them is d, then the eccentricity of the ellipse is given by e=(r1+r2)/d. The semiminor axis b is then given by , and that determines the shape of the ellipse.