If end points `t_1,t_2`, of a chord satisfy the relation `t_1 t_2 = 1` then chord always passes through the point if parabola is `y^2 = 4x`

Statement :1 If a parabola y ^(2) = 4ax intersects a circle in three co-normal points then the circle also passes through the vertex of the parabola. Because Statement : 2 If the parabola intersects circle in four points t _(1), t_(2), t_(3) and t_(4) then t _(1) + t_(2) + t_(3) +t_(4) =0 and for co-normal points t _(1), t_(2) , t_(3) we have t_(1)+t_(2) +t_(3)=0.

Statement :1 If a parabola y ^(2) = 4ax intersects a circle in three co-normal points then the circle also passes through the vertr of the parabola. Because Statement : 2 If the parabola intersects circle in four points t _(1), t_(2), t_(3) and t_(4) then t _(1) + t_(2) + t_(3) +t_(4) =0 and for co-normal points t _(1), t_(2) , t_(3) we have t_(1)+t_(2) +t_(3)=0.

The circle passing through the points (1, t), (t, 1) and (t, t) for all values of t passes through the point

The circle passing through the points (1, t), (t, 1) and (t, t) for all values of t passes through the point

The polar of the point (2t,t-4) w.r.t. the circle x^(2)+y^(2)-4x-6y+1=0 passes through the point

The polar of the point (2t,t-4) w.r.t. the circle x^(2)+y^(2)-4x-6y+1=0 passes through the point

The polar of the point (t-1, 2t) w.r.t. the circle x^(2)+y^(2)-4x+6y+4=0 passes through the point of intersection of the lines

What is the value of t such that P(t) and Q(3) are the end points of a focal chord of a parabola y^2 = 4ax ?