If a circle and the rectangular hyperbola `xy = c^(2)` meet in four points `'t'_(1) , 't'_(2) , 't'_(3) " and " 't'_(4)` then prove that `t_(1) t_(2) t_(3) t_(4) = 1`.

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.

If the normal to the rectangular hyperbola xy = c^2 at the point 't' meets the curve again at t_1 then t^3t_1, has the value equal to

If the normal to the rectangular hyperbola xy = 4 at the point (2t, (2)/(t_(1))) meets the curve again at (2t_(2), (2)/(t_(2))) , then

The normal to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

If a circle intersects the parabola y^(2) = 4ax at points A(at_(1)^(2), 2at_(1)), B(at_(2)^(2), 2at_(2)), C(at_(3)^(2), 2at_(3)), D(at_(4)^(2), 2at_(4)), then t_(1) + t_(2) + t_(3) + t_(4) is

The point of intersection of tangents at 't'_(1) " and " 't'_(2) to the hyperbola xy = c^(2) is

If the normal at point 't' of the curve xy = c^(2) meets the curve again at point 't'_(1) , then prove that t^(3)* t_(1) =- 1 .

If the normal at t_(1) on the parabola y^(2)=4ax meet it again at t_(2) on the curve then t_(1)(t_(1)+t_(2))+2 = ?

Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four points, three of them being (2, 2), (4, 1) and (6,2/3), then the coordinates of the fourth point are (1/4,16) . Statement 2 : If a circle S=0 intersects a hyperbola x y=c^2 at t_1,t_2,t_3, and t_3 then t_1-t_2-t_3-t_4=1

If the normal to the rectangular hyperbola x y=c^2 at the point (c t ,c//t) meets the curve again at (c t^(prime),c//t '),t h e n t^3t^(prime)=1 (B) t^3t^(prime)=-1 (C) t.t^(prime)=1 (D) t.t^(prime)=-1