- #1
arkkis
- 6
- 0
I have been struggling for a while now with this one.
Lets say I have two points on the arc of the ellipse. I know the y-coordinates and the difference of the x-coordinates. Is it possible two calculate the equation or the semiaxes of the ellipse where these points are located?
These are the information I can obtain. Actually the exact equation of the ellipse is not relevant. I should be able to calculate the ratio of the semi-axes.
EDIT: The ellipse is origo centered and the axes are parallel to x/y axes.
- - - -
Ellipse as a function of x:
x=sqrt[(a^2*b^2-a^2*y^2)/(b^2)]
So the difference of x-coordinates ie. deltax
deltax= x2-x1 =sqrt[(a^2*b^2-a^2*y2^2)/(b^2)] - sqrt[(a^2*b^2-a^2*y1^2)/(b^2)]
I guess somwhow I sould be able to eliminate a or b.
- - -
I also tried in a way where I know also the x-coordinates by solving a equation pair where i end up with:
a^4*(y2^2-y1^2)+a^2*(x2^2*y1^2-y2^2*x1^2)=0
I can't get it solved when just the x2-x1 is known.
- - -
Thanks!
Lets say I have two points on the arc of the ellipse. I know the y-coordinates and the difference of the x-coordinates. Is it possible two calculate the equation or the semiaxes of the ellipse where these points are located?
These are the information I can obtain. Actually the exact equation of the ellipse is not relevant. I should be able to calculate the ratio of the semi-axes.
EDIT: The ellipse is origo centered and the axes are parallel to x/y axes.
- - - -
Ellipse as a function of x:
x=sqrt[(a^2*b^2-a^2*y^2)/(b^2)]
So the difference of x-coordinates ie. deltax
deltax= x2-x1 =sqrt[(a^2*b^2-a^2*y2^2)/(b^2)] - sqrt[(a^2*b^2-a^2*y1^2)/(b^2)]
I guess somwhow I sould be able to eliminate a or b.
- - -
I also tried in a way where I know also the x-coordinates by solving a equation pair where i end up with:
a^4*(y2^2-y1^2)+a^2*(x2^2*y1^2-y2^2*x1^2)=0
I can't get it solved when just the x2-x1 is known.
- - -
Thanks!
Last edited: