Let $$E_{1} E_{2}$$ and $$F_{1} F_{2}$$ be the chords 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 to 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