A circle cuts the rectangular hyperbola `xy=1` in the points `(x_(1),y_(1)), r=1,2,3,4`.
Prove that `x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=1`

If the normal at four points P_(i)(x_(i), (y_(i)) l, I = 1, 2, 3, 4 on the rectangular hyperbola xy = c^(2) meet at the point Q(h, k), prove that x_(1) + x_(2) + x_(3) + x_(4) = h, y_(1) + y_(2) + y_(3) + y_(4) = k x_(1)x_(2)x_(3)x_(4) =y_(1)y_(2)y_(3)y_(4) =-c^(4)

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 (A) x_(1)+x_(2)+x_(3)+x_(4)=3 (B) y_(1)+y_(2)+y_(3)+y_(4)=4 (C) y_(1)y_(2)y_(3)y_(4)=4 (D) x_(1)x_(2)x_(3)x_(4)=-4

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

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points P (x_(1) ,y_(1)) Q (x_(2), y_(2)) R (x_(3) ,y_(3)) S (x_(4) ,y_(4)) then 1) x_(1)+x_(2)+x_(3)+x_(4)=2c^(2) 2) y_(1)+y_(2)+y_(3)+y_(4)=0 3) x_(1)x_(2)x_(3)x_(4)=2c^(4) 4) y_(1)y_(2)y_(3)y_(4)=2c^(4)

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) at four points P(x_(1),y_(1)),Q(x_(2),y_(2)),R(x_(3),y_(3)), and S(x_(4),y_(4)), then x_(1)+x_(2)+x_(3)+x_(4)=0y_(1)+y_(2)+y_(3)+y_(4)=0x_(1)x_(2)x_(3)x_(4)=C^(4)y_(1)y_(2)y_(3)y_(4)=C^(4)

If the normal at the point P(x_(i),y_(i)),i=1,2,3,4 on the hyperbola xy=c^(2) are concurrent at the point Q(h,k) then _((x_(1)+x_(2)+x_(3)+x_(4))(y_(1)+y_(2)+y_(3)+y_(4)))((x_(1)+x_(2)+x_(3)+x_(4))(y_(1)+y_(2)+y_(3)+y_(4)))/(x_(1)x_(2)x_(3)x_(4)) is

if the normals at (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),(x_(4),y_(4)) on the rectangular hyperbola xy=c^(2) meet at the point (alpha,beta). Then The value of (x_(1),+x_(2)+x_(3)+x_(4)) is