Greetings everyone, I am having difficulties grasping the polar form of the ellipse equation, and there seems to be more than one way to express an ellipse in this form, if I am not mistaken. For example on the following webpage http://farside.ph.utexas.edu/teaching/301/lectures/node155.html the ellipse is represented in a different way than I am accustomed. How can I convert this into other forms? Thanks
One option with the equation for an ellipse is whether to set the origin at a focus or at the centre. The link you provided gives the polar equation with a focus as origin. Do you have another link for contrast?
I do not have at the moment, I remember coming across one a year ago in a text I read. Do you have any site that I can learn conics and their equations in polar coordinates ?
Consider a string length 2L with endpoints fixed at (-A, 0), (+A, 0) (X-Y co-ords). With polar co-ordinates at the same origin, I get r^{2}(L^{2}-A^{2}.cos^{2}(θ)) = L^{2}(L^{2}-A^{2}) Does that look familiar? Converting back to X-Y: (x^{2}+y^{2})L^{2} - x^{2}.A^{2} = L^{2}(L^{2}-A^{2}) or x^{2}/L^{2} + y^{2}/(L^{2}-A^{2}) = 1 Which does indeed appear to be an ellipse centred at the origin.