Geometrical Theorems of a Parabola

Looking at two of the geometrical properties of a parabola

Chords of the Parabola

Finding the parametric equation of a chord

Using the features we have found, tangents, normals, chords and some key points, to discover some geometrical theorems of the parabola.

Generalising the equation of a chord of a parabola and the condition for it to be a focal chord.

Using parametrics to generalise the equation of a chord, as well as obtaining the condition for a focal chord.