Equations of Tangent and Normal to a Ellipse
Here we list the equation of tangent and normal for different forms of ellipse also we define parallel chords and condition of tangency of an ellipse:

Equation of tangent to the ellipse at is

Equation of normal to the ellipse at is

Equation of tangent to the ellipse at is

Equation of normal to the ellipse at is

The locus of middle points of parallel chords of an ellipse is the diameter of ellipse and has equation

The condition for to be the tangent to the ellipse is