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` is

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 four points P(x_(i)y_(i)),i=1,2,3,4 on the rectangular hyperbola xy=c^(2), meet at the point Q(h,k) prove that

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

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 = 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 the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.