If  $t_1,t_2,t_3$ are three variable parameters satisfying the relations $a{t}_2^2{t}_3^2=4b(t_2+t_3)$ and $a{t}_2^2{t}_1^2=4b(t_1+t_3),$ then the locus of the point of intersection of tangents to the parabola $y^2=4ax$  at $(a{t}_1^2,2a{t}_1)$  and $(a{t}_3^2,2a{t}_3)$  is