Help would be much appreciated with the following question.
The standard equation of a parabola is
y^2=4ax

A general point on this curve has co-ordianates x=at^2, y=2at where t is a (variable) parameter. A point P on the curve has co-ordinates x=a(t1)^2,

y=2a(t1). A chord is drawn through P to meet the parabola again at Q, which has co-ordinates x=a(t2)^2, y=2a(t2). If this chord passes through the focus S =(a,0) of the parabola find a simple relationship between (t1) and (t2).
Find the point at which the tangents to the parabola at P and Q meet.
(t1) is my notation for t with a subscript 1
(t2) is my notation for t with a subscript 2.