If $\left( m_{i},\frac{1}{m_{i}} \right),\ i = 1,\ 2,\ 3,\ 4$ are concyclic points, then the value of $m_{1}\ m_{2}\ m_{3}\ m_{4}$ is

Question

Dr. Abubacker · Accepted Answer

(a)
Let the equation of circle is
$x^{2} + y^{2} + 2gx + 2fy + c = 0$
Since, $\left( m,\frac{1}{m} ight)$ lies on this circle
$	herefore\ \ m^{2} + \frac{1}{m^{2}} + 2gm + \frac{2f}{m} + c = 0$
$\Rightarrow m^{4} + 2gm^{3} + cm^{2} + 2fm + 1 = 0$
$\Rightarrow m_{1}m_{2}m_{3}m_{4} = 1$

Q. If $\left( m_{i},\frac{1}{m_{i}} \right),\ i = 1,\ 2,\ 3,\ 4$ are concyclic points, then the value of $m_{1}\ m_{2}\ m_{3}\ m_{4}$ is

Explanation

Reviewed by Dr. Abubacker

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