Let S be the circle in the xy-plane defined by the equation x2+y2=4.Let E1E2 and F1F2 be the chords of S passing through the point P0(1,1) and parallel to the x-axis and the y-axis, respectively. Let G1G2 be the chord of S passing through P0 and having slope −1. Let the tangents to S at E1 and E2 meet at E3, the tangents to S at F1 and F2 meet at F3, and the tangents to S at G1 and G2 meet at G3. Then, the points E3,F3, and G3 lie on the curve

Let S be the circle in the xy-plane defined by the equation x2+y2=4.Le

1.	Let S be the circle in the xy-plane defined by the equation x2+y2=4.Let E1E2 and F1F2 be the chords of S passing through the point P0(1,1) and parallel to the x-axis and the y-axis, respectively. Let G1G2 be the chord of S passing through P0 and having slope −1. Let the tangents to S at E1 and E2 meet at E3, the tangents to S at F1 and F2 meet at F3, and the tangents to S at G1 and G2 meet at G3. Then, the points E3,F3, and G3 lie on the curve
Answer» Let $S$ be the circle in the $x y$ -plane defined by the equation $x^{2} + y^{2} = 4$ . 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