For different real non-zero numbers x₁, x₂, x₃ and x₄ , suppose the points (x₁, 1 x₁ ), (x₂, 1 x₂ ), (x₃, 1 x₃ ) and (x₄, 1 x₄ ) lie on the boundary of a circle of radius 4 . Then, the value of x₁ x₂ x₃ x₄ is

Step-by-step solution

Let the equation of the circle be x^2+y^2+2 g x+2 f y+c=0 (x_i, 1 x_i ) lies on the above circle. x_i^2+ 1 x_i^2 +2 g x_i+ 2 f x_i +C=0 aligned & x_i^4+2 g x_i^3+c x_i^2+2 f x_i+1=0 & x₁ x₂ x₃ x₄=1 aligned