A variable circle whose centre lies on `y^2 -36=0` cuts rectangular hyperbola `xy=16` at `(4t_i,4/t_i)e i=1,2,3,4` then `sum_(i=1)^4(1/t_i)` can be

The slope of the normal to the rectangular hyperbola xy=4 "at" (2t, (2)/(t)) is -

If the normals at (x_(i),y_(i)) i=1,2,3,4 to the rectangular hyperbola xy=2 meet at the point (3,4) then

If the normals at (x_(i),y_(i)) i=1,2,3,4 to the rectangular hyperbola xy=2 meet at the point (3,4) then

If the circle " x^(2)+y^(2)=1 " cuts the rectangular hyperbola " xy=1 " in four points (x_(i),y_(i)),i=1,2,3,4 then which of the following is NOT correct 1) " x_(1)x_(1)x_(3),x_(4)=-1 ," 2) " y_(1)y_(2)y_(3)y_(4)=1 3) " x_(1)+x_(2)+x_(3)+x_(4)=0 ," 4) " y_(1)+y_(2)+y_(1)+y_(4)=0

Let a circle x^(2) + y^(2) + 2gx + 2fy + k = 0 cuts a rectangular hyperbola xy = c^(2) in (ct_(1), c/t_(1)) , (ct_(2), c/t_(2)) , (ct_(3), c/t_(3)) " and " (ct_(4), c/t_(4)) .

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

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

If the circle x ^(2) +y^(2) =a^(2) intersects the hyperbola xy =c^(2) in four point (x_i,y_i) for i=1,2,3, and 4 then y_1+ y_2 +y_3 +y_4 =

A regular hexagon is drawn circumscribing the circle with centre (1,(1)/(sqrt(3))) and radius 2. (3,sqrt(3)) is one vertex and other vertices are (x_(i),y_(i)), i = 1,2,3,4,5 . Then, sum_(i=1)^(5)(x_(i)+y_(i)) is