Mid-point of chord on ellipse

Prove that the equation of the ellipse at the point is . The tangent at meets the tangent at at T. Show that the line

passes through T and through the midpoint of . Prove that if is a right angle, then

I have proven the first part. I got the equation of the tangent at in the same form as the first. Then I made y the subject of both tangents and found x. did it in the same way to find y.

I found the the line given passed through T, but could not prove that the line passed through the midpoint of , .

Thanks!