If (m_i, frac{1}{m_i}), i = 1, 2, 3, 4 are co | vedclass

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(A) Let the equation of the circle be $x^2 + y^2 + 2gx + 2fy + c = 0$.If the point $(m, \frac{1}{m})$ lies on this circle,then $m^2 + \frac{1}{m^2} +

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(A) Let the equation of the circle be $x^2 + y^2 + 2gx + 2fy + c = 0$.If the point $(m, \frac{1}{m})$ lies on this circle,then $m^2 + \frac{1}{m^2} + 2gm + \frac{2f}{m} + c = 0$.Multiplying by $m^2$,we get the equation $m^4 + 2gm^3 + cm^2 + 2fm + 1 = 0$.This is a fourth-degree equation in $m$ having $m_1, m_2, m_3, m_4$ as its roots.By Vieta's formulas,the product of the roots is given by the constant term divided by the leading coefficient.Therefore,$m_1 \cdot m_2 \cdot m_3 \cdot m_4 = \frac{1}{1} = 1$.

If $(m_i, \frac{1}{m_i}), i = 1, 2, 3, 4$ are concyclic points,then the value of $m_1 \cdot m_2 \cdot m_3 \cdot m_4$ is

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