The Negative Pell Equation y2 = 90x2 - 36: A Mathematical Observation

In this chapter, we have presented infinitely many integer solutions for the Diophantine equation, represented by hyperbola is given by y2 = 90x2 - 36 . The hyperbola represented by the binary quadratic equation y2 = 90x2 - 36 is analyzed for finding its non-zero distinct integer solutions. A few interesting relations among its solutions are presented. Also, knowing an integral solution of the given hyperbola, integer solutions for other choices of hyperbolas and parabolas are presented Also, employing the solutions of the given equation, special Pythagorean triangle is constructed. Diophantine equations come in a wide variety; one can look for further options and ascertain the integer solutions and appropriate features of those equations.