If (`m_r` ,`1/m_r`) where r=1,2,3,4, are four pairs of values of `x and y` that satisfy the equation `x^2+y^2+2gx+2fy+c=0` , then the value of `m_1. m_2. m_3. m_4` is a. 0 b. 1 c. -1 d. none of these

Options

A. 0
B. 1
C. -1
D. none of these

Answer

2

Explanation

If `[m_(r), (1//m_(r))]` satisfy the given equation
`x^(2) + y^(2) + 2gx + 2fy + c = 0`, then
`m_(r)^(2) + 1/m_(r)^(2) + 2gm_(r) + (2f)/(m_(r)) + c = 0`
`rArr m_(r)^(4) + 2gm_(r)^(3) + cm_(r)^(2) + 2fm_(r) + 1 = 0`
Now, roots of given equation are `m_(1), m_(2), m_(3), m_(4)`. The product of roots
`m_(1)m_(2)m_(3)m_(4) = ("Constant term")/("Coefficient of " m_(r)^(4)) = 1/1 = 1`