Chord of contact and Reflection property

Chord of Contact

Equation of chord of contact is T = 0, i.e. yy₁ = 2a(x + x₁) from an external point (x₁, y₁).

Equation of the chord of the parabola with mid point as (x1, y1) is

yy₁ − 2a(x + x₁) = y₁₂ − 4ax₁ or T = S₁.

Reflection property

Any ray parallel to the axis of the parabola will pass through focus after reflection.