Question

If(m_i,1/m_i);  i = 1, 2, 3, 4 are four distinct point on circle, show that m₁ m₂ m₃ m₄ = 1.

Answer 1

 Let the equation of circle be 

On substitution we get 

If m⁴ + 2gm³ + 2fm + cm² + 1 = 0 

m₁ , m₂ , m₃ , m₄ are roots of this equation 

then, m₁ m₂ m₃ m₄ = 1