In more advanced problems on the ellipse, you will need to know the equation of the directrix and the coordinates of the focus which are given in terms of the eccentricity e. I first give you a summary of these results and then the proofs.

Summary – Quick revision guide

The Ellipse - Quick revision guide : ExamSolutions Maths Revision - youtube Video

Proof: Equation of the directrix and coordinates of the focus

Ellipse - Equation of the directrix and coordinates of the focus : ExamSolutions Maths Revision - youtube Video

Proof: Cartesian equation of the ellipse

Ellipse - Cartesian equation Proof : ExamSolutions Maths Revision - youtube Video