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`

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 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 .

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 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

Find the coordinates o the vertices of a triangle, the equations of whose sides are: y(t_1+t_2)=2x+2a t_1a t_2,\ y(t_2+t_3)=2x+2a t_2t_3\ a n d\ , y(t_3+t_1)=2x+2a t_1t_3dot

The polars of two points A(1,3), B(2,-1) w.r.t to circle x^(2)+y^(2)=9 intersect at C then polar of C w.r.t to the circle is

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

If the tangent at a point P with parameter t , on the curve x=4t^2+3 , y=8t^3-1 t in R meets the curve again at a point Q, then the coordinates of Q are

If the tangent at a point P with parameter t , on the curve x=4t^2+3 , y=8t^3-1 t in R meets the curve again at a point Q, then the coordinates of Q are