P is a point on an ellipse whose major axis is AB the tangent at P meets the minor axis at Q. PA and PB cut the minor axis at R and T. Prove that Q bisects RT.

I put A=(a,0) and B=(-a,0)

equation of tangent at P

Point where tangent cuts minor axis, when x=o

equation AP

when x=0

equation BP

when x=0,

Now I don't know what to do. I can't show that RT=2RQ

Thanks!