JEE AdvancedCircleHard
Question
If 
are four distinct points on a circle of radius 4 units then, abcd =
are four distinct points on a circle of radius 4 units then, abcd = Options
A.4
B.1/4
C.1
D.16
Solution
Let equation of the circle be
x2 + y2 + 2gx + 2fy + λ = 0
(t, 1/t ) be a point on the circle
∴ t2 +
+ 2gt + 2f 
+ λ = 0
t4 + 2gt3 + λt2 + 2ft + 1 = 0
roots of the above equation are a, b, c & d
∴ abcd = 1
x2 + y2 + 2gx + 2fy + λ = 0
(t, 1/t ) be a point on the circle
∴ t2 +
+ 2gt + 2f + λ = 0t4 + 2gt3 + λt2 + 2ft + 1 = 0
roots of the above equation are a, b, c & d
∴ abcd = 1
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