Show that the tangent to the ellipse ax^2+by^2=1 at the point (h,k) has equation ahx+bky=1

Hence, deduce that the chord of contact of tangents from the point (m,n) to the ellipse ax^2+by^2=1 has equation amx+bny=1

I can do the 2 questions above.

Show that for all values of t, the chord of contact of tangents from the point (2t, 1-t) to the ellipse ax^2+by^2=1 passes through a fixed point and determine the point of this coordinates.

I am only stuck with this.