Question

How do we find center, major and minor axes, focii, vertices and eccentricity of an ellipse?

Answer 1

Please see below.

Explanation:

The standard equation of an ellipse is `(x-h)^2/a^2+(y-k)^2/b^2=1`

Its center is `(h,k)`

If `a>b`, the ellipse is horizontal and while major axis is `2a`, minor axis is `2b`. Vertices are `(h+-a,k)` and `(h,k+-b))`. Its eccentricity `e` is given by `e=sqrt(1-b^2/a^2)` and focii are `(h+-ae,k)`.

If `a<b`, the ellipse is vertical and while major axis is `2b`, minor axis is `2a`. Vertices are `(h+-a,k)` and `(h,k+-b))`. Its eccentricity `e` is given by `e=sqrt(1-a^2/b^2)` and focii are `(h,k+-be)`.