On the Binary Quadratic Diophantine Equation y2=80x2-16

Abstract

The Binary quadratic negative pell equation 16 80 2 2 − = x y representing a hyperbola is analyzed for its non-zero integer solutions. A few interesting relations among its solutions are presented. Further, employing the solutions of the above equation, we have obtained solutions of other choices of hyperbolas, parabolas and special pythogorean triangles.