If `(x_i , 1/x_i), i = 1, 2, 3, 4` are four distinct points on a circle, then (A) `x_1 x_2 = x_3 x_4` (B) `x_1 x_2 x_3 x_4 = 1` (C) `x_1 + x_2 + x_3 + x_4 = 1` (D) `1/x_1 + 1/x_2 + 1/x_3 + 1/x_4 = 1`

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 : (A) x_1 + x_2 + x_3 + x_4 = 0 (B) y_1 + y_2 + y_3 + y_4 = 0 (C) x_1 x_2 x_3 x_4= c^4 (D) y_1 y_2 y_3 y_4 = c^4

If x_1 x_2 x_3 = 4(4 + x_1 + x_2 + x_3 ) , then what is the value of [1//(2 + x_1 )] + [1//(2 + x_2 )] + [1//(2 + x_3 )] ?

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 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)

The equation x^(4) -2x^(3) - 3x^(2) + 4x-1=0 has four distinct real roots x_1,x_2,x_3,x_4 such that x_1 lt x_2 lt x_3 lt x_4 and product of two roots is unity , then : x_1x_2+x_1x_3 + x_2x_4+x_3x_4 is equal to :

The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roots x _(1), x _(2), x _(3), x_(4) such that x _(1) lt x _(2) lt x _(3)lt x _(4) and product of two roots is unity, then : x _(1)x _(2) +x_(1)x_(3) + x_(2) x _(4) +x_(3) x _(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

Find the value of ( 1 + 1/x ) ( 1 + 1/( x+1 )) ( 1 + 1/( x+2 ) ) ( 1 + 1/( x+3 )) is : (1) 1 + (1/(x + 4 )) ( 2 ) x +4 ( 3 ) 1/x ( 4 ) ( x+4 )/x

(1) / (x + 1)-(2) / (x ^ (4) -x + 1) <(1-2x) / (x ^ (3) +1)