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 which of the following need not hold.
(a)  `x_1+x_2+x_3+x_4=0`
(b)  `x_1 x_2 x_3 x_4=y_1 y_2 y_3 y_4=c^4`
(c)  `y_1+y_2+y_3+y_4=0`
(d)  `x_1+y_2+x_3+y_4=0`