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
Create a free account to view solution
View Solution FreeMore Circle Questions
The circle x2 + y2 + 2gx + 2fy + c = 0 bisects the circumference of the circle x2 + y2 + 2ax + 2by + d = 0, then -...If point p(α + 1, α) lies between the ellipse 16x2 + 9y2 - 16x = 0 and its auxiliary circle, then -...The parametric coordinates of any point on the parabola y2 = 4ax can be -...The greatest distance of the point P(10, 7) from the circle x2 + y2 - 4x - 2y - 20 = 0 is -...The tangent from the point of intersection of the lines 2x - 3y + 1 = 0 and 3x - 2y - 1 = 0 to the circle x2 + y2 + 2x -...