QJEEAdv18Ma5cf0: JEE Advanced 2018 Mathematics - Class 11 JEEAdv18Ma5cf0 Solution: Let S be the circle in the XY-plane defined the equation x 2 +…

Equation of tangent at ${E_1}( - \sqrt 3 ,1)$ is

$- \sqrt 3$ x + y = 4 and at ${E_2}(\sqrt 3 ,1)$ is $\sqrt 3$ x + y = 4

Intersection point of tangent at E₁ and E₂ is (0, 4)

$\therefore$ Coordinates of E₃ is (0, 4)

Similarly, equation of tangent at

${F_1}(1, - \sqrt 3 )$ and ${F_2}(1,\sqrt 3 )$ are x $-$ $\sqrt 3$ y = 4 and

x + $\sqrt 3$ y = 4, respectively and intersection point
is (4, 0), i.e., F₃(4, 0) and equation of tangent at G₁(0, 2) and G₂(2, 0) are 2y = 4 and 2x = 4, respectively and intersection point
is (2, 2) i.e., G₃(2, 2).

Point E₃(0, 4), F₃(4, 0) and G₃(2, 2) satisfies the line x + y = 4.