On the hyperbola X$^2$+4XY+Y$^2$-2X+2Y-8=0

S. Vidhyalakshmi, 1 *, M.A. Gopalan 2 and S. Aarthy Thangam 3

doi:10.26637/MJM0S01/0001

On the hyperbola X$^2$+4XY+Y$^2$-2X+2Y-8=0

Authors :

S. Vidhyalakshmi, ^{1 *}, M.A. Gopalan ² and S. Aarthy Thangam³

Author Address :

^1,2,3Department of Mathematics, Shrimati Indira Gandhi College, Trichy-620002, Tamil Nadu, India.

*Corresponding author.

Abstract :

We search for the lattice points of the hyperbola $X^2+4XY+Y^2-2X+2Y-8=0$. Various connections among the solutions are given. Given a solution, solutions for other forms of hyperbolas and parabolas are determined.

Keywords :

Binary quadratic, Hyperbola, Parabola, Pell equation, Integral solutions.

DOI :

10.26637/MJM0S01/0001

Article Info :

Received : December 21, 2018; Accepted : February 11, 2019.