Let the points `(m_(i),(1)/(m_(i))),i = 1,2,3,4`
lie on a circle `x^(2) | y^(2)+2gx+2fy+c-0`.
Then, `m_(i)^(2)+(1)/(m_(i)^(2))+2gm_(i)+(2f)/(m_(i))+c=0`,
Since, `m_(i)^(4)+2gm_(i)^(3)+cm_(i)^(2)+2fm_(i)+1=0, i=1,2,3,4`
`rArr m_(1), m_(2), m_(3) and m_(4)` are the roots of the equation
`m^(4)+2gm^(3)+cm^(2)+2fm+1=0`
`rArr" " m_(1)m_(2)m_(3)m_(4)=(1)/(1)=1`
