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If (a,1/a), (b,1/b),(c,1/c),(d,1/d) are four distinct points on a circle of radius 4 units then,abcd is equal to??

If (a,1/a), (b,1/b),(c,1/c),(d,1/d) are four distinct points on a circle of radius 4 units then,abcd is equal to??

Grade:12

2 Answers

konduri abhilash reddy reddy
18 Points
8 years ago

 

1

as they are of form (x,1/x)

let eq of circle be x2+y2+2gx+2fy+c=0

it passae through general pt (x,1/x)

substituting we get 4th degree in x

a,b,c,d are roots of it

by theory of equations it is constant term/coefficient of x2

then it comes to be 1

Nishant Kumar
9 Points
2 years ago
Consider only the a, b, c and d .  They are the roots of the equation when we put (x, 1/x) in the general equation of circle . CLEAR. now, We will get a 4 degree equation on solving that. In a 4 degree equation PRODUCT OF ROOTS (i. e.  abcd) =1 . 
Regards
NISHANT BOW

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