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If(a,1/a),(b,1/b), (c,1/c) & (d,1/d) are...

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
(A) `4` (B) `16`
(C) `1` (D) `2`

Text Solution

Verified by Experts

Standard equation of a circle is
`x^2+y^2+2gx+2fy+c = 0`
Let, `(m,1/m)` lies on this circle, then
`m^2+1/m^2+2gm+2f/m+c = 0`
`=>m^4+1+2gm^3+2fm+cm^2 = 0`
`=>m^4+2gm^3+cm^2+2fm+1= 0->(1)`
Let `m_1,m_2,m_3,m_4` are the roots of equation (1), then,
`m_1*m_2*m_3*m_4 = (1/1)**(-1)^4 = 1`
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