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Let E_(1)E_(2) and F_(1)F_(2) be the chords of S passing through the point P_(@) (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_(@) and having slope -1. Let the tangents to S at E_(1)and E_(2) met 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 Let S be the circle in the XY-plane defined by the equation x^(2)+y^(2)=4 |
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Answer» x + y = 4  Equation of tangent at `E_(1)(-sqrt3,1)` is `-sqrt3x +y=4 and "at" E_(2)(sqrt3,1)` is `sqrt3x+y=4` Intersection point of tangent at`E_(1) and E_(2) " is " (0,4)`1. `THEREFORE` Coordinates of `E_(3)` is (0, 4) Similarly equation of tangent at`F_(1)(1, -sqrt3) and F_(2)(1,sqrt3)` are `x-sqrt3y=4 and x+sqrt3y=4`, respectively and intersection point is (4, 0), i.e., `F_(3)(4,0)` and equation of tangent at `G_(1)(0,2) and G_(2)(2,0)` are 2y =4 and 2X = 4, respectively and intersection point is (2, 2)i.e., `G_(3) (2,2)`. Point `E_(3) (0, 4) , F_(3)(4,0) and G_(3)(2, 2)` satisfies the line x + y = 4. |
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