If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i,y_i),$ for $i=1,2,3$ and $4$, then $y_1+y_2+y_3+y_4=$

Question

$$\begin {array} {1 1} (1)\;0 & \quad (2)\;c \\ (3)\;a & \quad (4)\;c^4 \end {array}$$