Let S be the circle in the xy-plane defined by the equation x 2 + y 2 = 4.
(i)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, then, the points E 3 , F 3 , and G 3 lie on the curve
Text Solution
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(i) Tangent at E 1 and E 2 are 
and 
They intersect at E 3 (0, 4)
F 1 (1, 
), F 2 (1, – 
), F 3 (4, 0)
G 1 (0, 2), G 2 (2, 0), G 3 (2, 2)
E 3 , F 3 , G 3 lie on line x + y = 4
E 3 , F 3 , G 3 x + y = 4
(ii) Let P(2 cos θ , 2 sin θ )
Tanget is x cos θ + y sin θ = 2
M 
, N 
x = 
and y = 
⇒ 
+ 
= 1 ⇒ x 2 + y 2 = x 2 y 2
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