M.A. Gopalan, S. Vidhyalakshmi, V. Pandichelvi, P. Sivakamasundari, C. Priyadharsini, On the Negative Pell Equation y2=45x2-11, Volume 16, International Journal of Pure Mathematical Sciences (Volume 16) https://www.scipress.com/IJPMS.16.30 Abstract: The binary quadratic equation represented by the negative pellian y<sup>2</sup>=45x<sup>2</sup>-11 is analyzed for its distinct integer solutions. A few interesting relations among the solutions are also given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and special Pythagorean triangle. Keywords: Binary Quadratic, Hyperbola, Integral Solutions, Parabola, Pell Equation