Paragraph: Let S be the circle in the x y – plane defined by the equation x 2 + y 2 = 4 . Question : 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

Step-by-step solution

Co - ordinates of E 1   a n d   E 2 are obtained by solving y = 1   a n d   x 2 + y 2 = 4 ∴     E 1 - 3 ,   1   a n d   E 2 3 ,   1 Co - ordinates of F 1   a n d   F 2 are obtained by solving x = 1   a n d   x 2 + y 2 = 4 F 1 1 ,   3   a n d   F 2 1 , - 3 Tangent at E 1 :   - 3 x + y = 4 Tangent at E 2 :   - 3 x + y = 4 ∴ E 3 0 ,   4 Tangent at F 1 : x + 3 y = 4 Tangent at F 2 : x - 3 y = 4 ∴