Let S be the circle in the xy-plane defined by the equation  $x^2+y^2=4$. Let $E_1{E}_2$ and $F_1{F}_2$ be the chord of S passing through the point $P_0(1,1)$ and parallel to the x-axis and the y-axis, respectively. Let $G_1{G}_2$ be the chord of S passing through $P_0$ and having slope -1. Let the tangents to S at $E_1$ and $E_2$ meet at  $E_3$, the tangents of S at $F_1$ and $F_2$ meet at $F_3$, and the tangents to S at $G_1$ and $G_2$ meet at  $G_3$. Then, the points $E_3, F_3 and G_3$ lie on the curve