I can't understand eccentricity of conic sections intuitively ,is there an elegant way to put it ?
Eccentricity is given by
$e$=$\sqrt{(1-\frac{b²}{a²})}$
But why ?
Why does it matter that we take the ratio of two random lines?
What does it say about the curve ?
Why does it matter that we take the ratio of two distances mentioned in the picture ,?