A circle cuts the curve `xy=c^2`, in four points `(x_i, y_i), i = 1, 2, 3, 4` then (A) `prodx_1 = prody_1 = 4c^4` (B) `prodx_1 = prody_1 = c^4` (C) `prodx_1 = prody_1 = 4c^2` (D) `prodx_1 = prody_1 = c^2`

Tangent are drawn from two points (x_1, y_1) and (x_2, y_2) to xy = c^2 . The conic passing through the two points and through the four points of contact will be circle if (A) x_1 x_2 = y_1 y_2 (B) x_1 y_2 = x_2 y_1 (C) x_1 y_2 + x_2 y_1 = 4c^2 (D) x_1 x_1 + y_1 y_2 = 4c^2

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 (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)=r^(2) intersects the hyperbola xy=c^(2) in four points (x_(i),y_(i)) for i=1,2,3 and 4 then y_(1)+y_(2)+y_(3)+y_(4)=

If the line y=x touches the curve y=x^2+b x+c at a point (1,\ 1) then (a) b=1,\ c=2 (b) b=-1,\ c=1 (c) b=2,\ c=1 (d) b=-2,\ c=1

If ((1 +i)/(1 -i))^(x) =1 , then (A) x=2n+1 (B) x=4n (C) x=2n (D) x=4n+1, n in N.

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)

For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is (a) 1//2 (b) 1 (c) -1 (d) 2

For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is 1//2 (b) 1 (c) -1 (d) 2

Find x such that the four points A\ (3,\ 2,\ 1) , B(4, x ,\ 5) , C\ (4,\ 2,\ 2) and D\ (6,\ 5,\ 1) are coplanar