*Short Communication*Year: 2015 | Month: April | Volume: 2 | Issue: 4 | Pages: 183-188

**On The Negative Pell Equation**** y ^{2} = 35x^{2}-19 **

M.A. Gopalan^{1}, S.Vidhyalakshmi^{1}, T.R. Usharani^{2}, M. Arulmozhi^{3}

^{1}Professor, ^{2}Lecturer, ^{3}PG Student,

Department of Mathematics, SIGC, Trichy-620002, Tamilnadu, India.

Corresponding author: M.A. Gopalan

**ABSTRACT**

The negative Pell equation represented by the binary quadratic equation y^{2} = 35x^{2}-19 is analyzed for its non-zero distinct integer solutions. A few interesting relations among the solutions are presented. Employing the solutions of the equation under consideration, the integer solutions for a few choices of hyperbola and parabola are obtained.

** Keywords: **Binary quadratic, Hyperbola, Parabola, Integral solutions, Pell equation. 2010 Mathematics subject classification:11D09.