could anyone explain the highlighted part, why do things change if b > a? (why is the y-axis the major axis)
eccentricity & ellipses Watch
- Thread Starter
- 08-04-2013 20:14
- Political Ambassador
- 08-04-2013 20:33
Set x and y, in turn, to zero and see how this condition affects the points at which the ellipse crosses the axesLast edited by Indeterminate; 08-04-2013 at 20:36.
- 08-04-2013 23:35
Rather than having two equations to cover the two cases, you just note that a reflection in x = y changes direction of the major axis. If it was initially along the x-axis, reflection in that line will put it along the y-axis and vice versa. The reflection will necessarily change the position of the foci and directrices as well.
If the equation was completely symmetric then it would not matter which of a and b was larger, but since they are different for an ellipse (excluding the case where it is actually a circle) it clearly matters which is larger. That lack of symmetry is really the key.
Note that for so you cannot have if . That would be a contradiction.